Austria’s Chancellor Sebastian Kurz, a conservative leader who governs in coalition with an anti-immigration party, on Friday announced the closure of seven mosques and the potential expulsion of 40 imams, in a crackdown on political Islam and foreign funding of Muslim communities.

The move follows a government investigation into alleged radical activities in mosques that was ordered after a series of revelations in the media about extremist preachers. In one incident, images published by a newspaper in April showed young...