Upvote:1
Assuming you mean the Republic of Cyprus (the southern/Greek, internationally recognized part):
Cyprus is not in the Schengen area, but as a "future joiner" state it does apply some Schengen rules. One of these rules is that holders of residence permits from any Schengen countries are exempt from needing a visa for short visits.
See http://www.mfa.gov.cy/mfa/embassies/embassy_copenhagen.nsf/page09_en/page09_en?OpenDocument
So you do not need a visa, but you should bring both your passport and your Danish residence card.