PARIS — In its boldest development in a generation, the Louvre Museum has a new wing dedicated to Islamic art, a nearly €100 million ($130 million) project that comes at a tense time between the West and the Muslim world.

Louvre curators tout their new Islamic Art department, which took 11 years to build and opens to the public on Saturday, as a way to help bridge cultural divides. They say it offers a highbrow and respectful counterpart to the recent unflattering depictions of the Prophet Muhammad in Western media that have sparked protests by many Muslims.

Still, one of the Louvre’s own consultants acknowledged that some Muslims could be “shocked” by three images of Muhammad with his face exposed in the new wing. Many Muslims believe the prophet should not be depicted at all — even in a flattering way — because it might encourage idolatry....