Referring to the Prince from Sands of Time, there are strong implications, given the references Vizier, a Muslim scholar serving a monarch, and Sultan, a ruling monarch who is Muslim. It’s also shown that Sharaman, the Father of the Prince was well-respected by the Sultan of Azaad. It’s also true that the villainous Vizier is the Uncle of the Prince and Brother of his Father, King Sharaman, making it likely that Sharaman, by family ties, and political trust to the Vizier is likely, also Muslim, being able to have a close trust to his Muslim Brother who served as an advisor to the Indian Ruler and father of the Princess Farah. It’s never clear-cut with words like Allah, left out of the Prince of Persia games, but the family connections, and nobility shared between the Vizier and Sharaman, as well as between Sharaman and the Sultan it is strongly implied.
In the 2008 game Prince of Persia, the Prince of that game is definitively Zoroastrian, and not Muslim, the game also outlines Zoroastrian mythology, with the Tree of Life, and the opposing Gods of Creation and Destruction, outlining the game’s mythology.