Did the early Christian community on Iceland require the import of wine for liturgy?

The Church has always required that the matter for transubstantiation be wine made from grapes. This has be codified under:

Can. 924

§1. The most holy eucharistic sacrifice must be offered with bread and with wine in which a little water must be mixed.

§2. The bread must be only wheat [not barley, etc.] and recently made so that there is no danger of spoiling.

§3. The wine must be natural from the fruit of the vine and not spoiled.

Even must (barely fermented, unprocessed, unadulterated grape juice) can be used, if necessary.

If Icelanders don't have wine or wheat, they must obtain them somehow. This is generally what's done today. Much of the altar wine used in the U.S., for example, is imported from California (cf. Cribari). The same goes for altar bread. In the early missions in the southwest U.S., for example, vineyards were cultivated, some of which still exist today.

A sacrament with improper matter (e.g., baptism with motor oil, barley and apple juice in the Eucharist, etc.) is invalid.

Referenced in the Wittmann, P., & Remy, A.F.J. (1910). Iceland. In The Catholic Encyclopedia, the following work describes the Icelandic discovery of America ("Wineland"):

• The Finding of Wineland the Good: The History of the Icelandic Discovery of America (1890) by Reeves, Arthur Middleton, 1856-1891

Short answer

Wine was imported but was often scarce and always expensive. It was a liturgical requirement, but it was not one that was always (or even often) met without bending the rules a little.

When supplies ran out or low, substitutes were used, though by the first half of the 13th century the popes were clamping down on this practice. Given the distances involved and the reality of the situation with which priests in Iceland were faced, the popes' word was not strictly followed, though. There is direct evidence from the 14th century that wine was watered down, and mass was sometimes held without wine.

Details

Orri Vesteinsson, in The Christianization of Iceland: Priests, Power, and Social Change 1000-1300 notes that we have limited evidence but cites the case of a priest Reginpreht bringing wine to Iceland:

The Old German eleventh-century poem Merigarto mentions an excellent, learned, and honourable priest called Reginpreht whom the author had met in Utrecht and who had been to Iceland and profited greatly from selling grain, wine, and timber.

In the 11th century especially, there were frequent visits to Iceland by bishops, priests and monks from Norway. They may well have brought supplies with them. In the 13th century, there is evidence of wine being sent to Iceland as a gift:

...in a charter dated 1277, in Skallholt, it is stated..."that the bishop thanks him for the friendly words and the present which the king has sent him [of a] barrel of wine for the mass and a pound of wax and a pound of flour"

Source: Jesus Fernando Guerrero Rodriguez, 'Old Norse Drinking Culture' (2007 Doctoral thesis)

Also, in 1279, King Magnus VI of Norway

send[s] two barrels of wine to Bishop Arni Porlaksson

Source: Rodriguez

There is also evidence of wine imports (and the high price) from a 1420 charter in Vestmannaeyjar, Iceland:

It provides a price-list for trade between Icelandic and English merchants. According to it, one could acquire "iiij tunnur biors firir hundrat" (four barrels of bjarr for a hundred) while one would get "tunna vins firir klent .C." (a barrel of vin for a clean hundred). In other words, one could acquire 4 barrels of bjarr for the price of a milch cow or two marks and a half (i.e. 570 gr.) of silver, while a single barrel of wine would cost four times as much (roughly 2.3 kg. of silver as pure as that used to pay for the four barrels of bjarr). That is, a barrel of wine was 16 times more expensive than a barrel of bjarr.

Source: Rodriguez

Other cases of imported wine are mentioned in the source provided in Nathan Cooper's comment:

...limited quatities of such beverages as wine, mead, and beer were imported, mostly from Germany. Earlier, wine had been purchased from England....

Source: Jón Jóhannesson, 'A History of the Old Icelandic Commonwealth: Islendinga Saga'

Nonetheless, wine was sometimes in short-supply

when trading-vessels failed to arrive. For this reason Icelanders began in 1203 to make berry-wine as a substitute for communion-wine. Bishop Jon of Greenland taught the Icelanders how to make this wine from crowberries....Berry-wine was then used for communion services to some extent until 1237, when the Pope forbade...

Source: Jón Jóhannesson

Wine was, unsurprisingly, very expensive. In Norway and Sweden, beer and heavily watered wine were used (and then banned by the pope). Many bishops and priests came to Iceland from Norway and brought these practices with them. Perhaps unwisely (as semaphore suggests in a comment), rather than keeping quiet about it,

In 1237 the archbishop of Nidaros, Sigurd Eindridesson (r. 1231–52), tried to convince Pope Gregory IX (r. 1227–41) that his most northern frontier needed special assistance because wheat and wine could not be produced locally. He even suggested replacing wine in the sacrament with beer or some other liquid. But the pope did not agree. The province of Nidaros, which consisted of Norway, Greenland, Iceland, and other North Atlantic islands, had to follow the same rules as all other Christian territories.

Source: Lars Bisgaard, 'Wine and Beer in Medieval Scandinavia'. In Kirsi Salonen, Kurt Villads Jensen, and Torstein Jørgensen (eds), 'Medieval Christianity in the North' (2013)

To what extent the Icelandic priests obeyed the pope is unclear, but they certainly watered the wine (see below). Not only was wine very expensive and Iceland even further away from its production centres than Norway, but also archaeological evidence indicates that Iceland was comparatively poor:

Orri 0steisson has noted...in the archaeological record) "[o]ne has to go pretty far down on the social scale of Norwegian (burials to find graves that compare with the richest Icelandic ones"

Source: Megan Arnott, 'Hveiti ok Hunang: Viking Age Icelandic Mead?'

Taking all the (limited) evidence into consideration, it is likely that, although wine for liturgical purposes was used when available, it was probably restricted both in the number of people who used it (mostly priests) and the frequency, and that substitutes (most likely beer) were sometimes used despite the pope's strong disapproval. Also, evidence of watering comes from a charter written in the 1320s:

in a charter written ca. 1323-28 it is stated that:..."([we] order also that all the priests, under the penalty of suspension from the office, that only them sing mass [and that] only the priest that sings mass blends water with wine in the chalice, and not the clerk, so that there is more water than wine in the chalice so that water is more abundant than wine."

Source: Rodriguez

Rodriguez also cites

A charter dated 1375, begins with the words "af pui ath vijn hefir ecki et cetera, (because we have no wine et cetera) instructs the priests to continue with the celebration of mass every Sunday.

(All emphasis is mine)