A geocentric model can accommodate this phenomenon perfectly fine, as long as it accepts that 1) the earth is round, and 2) that orbits can shift throughout the year. Given that scholars in both ancient and medieval Europe acknowledged both of these facts, they explained the Arctic midnight sun as a purely natural phenomenon.

It's unclear whether or not ancient references to the island of Thule refer to Iceland, the Shetlands, the Faroes, or some other unidentified island in the far north, but ancient discussions of it are relevant here. Pytheas of Massalla (4th century BCE) wrote a now lost but widely cited geography of the far north, in which he described Thule as lying at the utmost northern extreme of the Ocean, with nights and days that could last six months. His description was widely referenced and elaborated by successive geographers, such as Strabo and Pliny the Elder. Strabo happened to think that Pytheas was full of it, disbelieving most of he wrote about Thule. Nonetheless, he conceded that the description of long days/nights was consistent with contemporary models of astronomy and geography:

And yet, if judged by the science of the celestial phenomena and by mathematical theory, he might possibly seem to have made adequate use of the facts as regards the people who live close to the frozen zone, when he says that, of the animals and domesticated fruits, there is an utter dearth of some and a scarcity of the others, and that the people live on millet and other herbs, and on fruits and roots; and where there are grain and honey, the people get their beverage, also, from them. As for the grain, he says, — since they have no pure sunshine — they pound it out in large storehouses, after first gathering in the ears thither, for the threshing floors become useless because of this lack of sunshine and because of the rains. (Geographica 4.5.5)

Pliny the Elder was more inclined to take Pytheas at his word, and elaborated on why there should be such long days and nights in these northern latitudes. Since the earth was spherical, and objects near the equator cast no shadow at certain times of the year, Pliny figured that the length of days must vary both across latitude and across time. Thus, when discussing Thule, he writes:

During the solstitial period, as the sun approaches to the pole of the world, and his orbit is contracted, the parts of the earth that lie below him have a day of six months long, and a night of equal length when he is removed to the south pole. Pytheas, of Marseilles, informs us, that this is the case in the island of Thule, which is six days' sail from the north of Britain. (Naturalis Historia 2.77)

Later in the Naturalis Historia:

The most remote of all that we find mentioned is Thule, in which, as we have previously stated, there is no night at the summer solstice, when the sun is passing through the sign of Cancer, while on the other hand at the winter solstice there is no day. (4.30)

As you can see from Pliny's description, his model is geocentric (the sun approaches the pole), but the basic facts of the midnight sun are intact. Very few of these classical authors ever had occasion to actually travel this far north, but their accounts of Thule and its strange natural phenomena were well-known by the time that Europeans actually discovered and settled Iceland.