The summary in Mike's answer seems accurate. I would like to add some further background and primary sources.

Evidently, Calvin felt it necessary to write to Sir William Cecil, Queen Elizabeth I's chief adviser, when Calvin's messenger told him that the queen was unhappy with Calvin because of Knox's Monstrous Regiment, which was written in Geneva. In reply, Calvin denounced the treatise as Knox's "ravings":

I am indeed exceedingly and undeservedly grieved, in proportion to my surprise, that the ravings of others, as if on a studied pretext, should be charged upon me.

He was not aware of the book's publication until it had already been widely circulated, but he hoped that ignoring it would help it to disappear:

When I was informed of it by certain parties, I sufficiently shewed my displeasure that such paradoxes should be published; but as the remedy was too late, I thought that the evil which could not now be corrected, should rather be buried in oblivion than made a matter of agitation.

When Knox had asked Calvin what he thought of women in government, Calvin replied that it was a tragic effect of the fall, but that sometimes God ordained it and raised up specific women for the purpose, and that rebellion is not the right thing to do anyway:

Two years ago John Knox asked of me, in a private conversation, what I thought about the government of women. I candidly replied, that as it was a deviation from the original and proper order of nature, it was to be ranked, no less than slavery, among the punishments consequent upon the fall of man; but that there were occasionally women so endowed, that the singular good qualities which shone forth in them, made it evident that they were raised up by divine authority; either that God designed by such examples to condemn the inactivity of men, or for the better setting forth his own glory. I brought forward Huldah and Deborah; and added, that God did not vainly promise by the mouth of Isaiah, that queens should be the nursing mothers of the church; by which prerogative it is very evident that they are distinguished from females in private life. I came at length to this conclusion, that since both by custom and public consent and long practice it has been established, that realms and principalities may descend to females by hereditary right, it did not appear to me necessary to move the question, not only because the thing would be invidious, but because in my opinion it would not be lawful to unsettle governments which are ordained by the peculiar providence of God.

Apparently, Calvin regarded Elizabeth as one of the women specially raised up by God for government:

I shall always reverence both the most serene queen, and shall not cease, most illustrious sir, to love and respect yourself also.

You can read the whole letter here.

Appendix: Earlier conversation between Calvin and Knox about women in government

(As I was writing this answer, I mistakenly thought the below was the conversation Calvin alluded to in the letter above. Calvin tells Cecil that his conversation with Knox happened in 1557, whereas the below letters were written in 1554 about conversations that happened earlier that year. Still, you may find them worthwhile reading, since they have similar subject matter. I suppose it is also possible that Calvin was mistaken on when the conversation took place, and that the conversation he describes to Cecil actually happened in 1554.)

In God's Watchman: John Knox's Faith and Vocation (pg. 200) by Richard Kyle, it's described how Knox asked Calvin and Heinrich Bullinger in 1554 for their thoughts on certain questions that he would treat in The Monstrous Regiment in 1558:

He [Knox] left Dieppe and first arrived in Geneva some time in March 1554 and immediately approached Calvin with certain questions regarding disobedience. Calvin received Knox cordially, answered his questions verbally, and sent him on to Viret in Lausanne and finally to Bullinger in Zurich. Knox submitted four specific questions to Calvin, Bullinger, and presumably Viret.

Bullinger later wrote Calvin to show him what he had told Knox and get his feedback, and Calvin replied with a comparison of what he had told Knox himself. In the following, I will quote excerpts of both letters, first with Kyle's paraphrase of Knox's four particular questions, then with Bullinger's reply to Knox, then Calvin's reply to Bullinger:

Knox: Was the son of a king who inherited the throne as a minor a lawful magistrate and thus deserving of obedience by divine right?

Bullinger: That person is, in my opinion, to be esteemed as a lawful King, who is ordained according to the just laws of the country. And thus it is clear that Edward VI. of happy memory was ordained.

Calvin: Respecting hereditary succession in monarchies, I had taken nearly the same view as yourself.

Knox: Could a woman ruling by divine right transfer the authority to her husband?

Bullinger: The law of God ordains the woman to be in subjection, and not to rule; which is clear from the writings of both the Old and the New Testament. But if a woman in compliance with, or in obedience to the laws and customs of the realm, is acknowledged as Queen, and, in maintenance of the hereditary right of government, is married to a Husband, or in the mean time holds the reins of government by means of her councillors, it is a hazardous thing for godly persons to set themselves in opposition to political regulations. ... With respect, however, to her right of transferring the power of government to her Husband, those persons who are acquainted with the laws and customs of the realm can furnish the proper answer.

Calvin: About the government of women I expressed myself thus: Since it is utterly at variance with the legitimate order of nature, it ought to be counted among the judgments with which God visits us; and even in this matter his extraordinary grace is sometimes very conspicuous, because to reproach men for their sluggishness, he raises up women endowed not only with a manly but a heroic spirit, as in the case of Deborah we have an illustrious example. But though a government of this kind seems to me nothing else than a mere abuse, yet I gave it as my solemn opinion, that private persons have no right to do anything but to deplore it. For a gynaecocracy or female rule badly organized is like a tyranny, and is to be tolerated till God sees fit to overthrow it. ... It is our duty rather to ask God for a spirit of moderation and prudence, to stand us in aid in the critical moment, than to agitate idle enquiries.

Knox: Must people obey a magistrate who sought to enforce idolatry, and may local authorities holding a town by force lawfully resist such orders?

Bullinger: We must not obey the king or magistrate when their commands are opposed to God and his lawful worship; but rather that we should expose our persons, and lives, and fortunes to danger. [Bullinger then mentions that in the past, some Christians have violently rebelled against ungodly rulers.] An accurate knowledge of the circumstances is here of great importance; and as I do not possess such knowledge, it would be very foolish in me to recommend or determine any thing specific upon the subject. There is need, therefore, in cases of this kind, of much prayer, and much wisdom.

Calvin: On the second head—whether it is lawful for us to uphold the Gospel by force of arms, there was not the least discrepancy between our ideas.

Knox: May Christians lawfully support a nobility who are resisting an idolatrous ruler?

Bullinger: I leave this to be decided by the judgment of godly persons, who are well acquainted with all the circumstances, who look up in all things to the Word of God, who attempt nothing contrary to the laws of God, who obey the impulses of the Holy Ghost, and who are guided by circumstances of place, time, opportunity, persons, and things, without making any rash attempt, and who can therefore be directed more safely by their own sense of duty than by the consciences of others.

[Calvin did not tell Bullinger his answer to this question, because he was in a hurry]: Since the time that I found fitting messengers to whom I might venture to entrust my letter, I have been prevented by the pressure of other business from continuing it, as I should have wished, any further. Farewell then.