Regal Entertainment Group and AMC Entertainment Holdings Inc., the nation’s two largest movie theater chains, have received formal inquiries from the Justice Department’s Antitrust Division, signaling growing government scrutiny of a tactic large theater operators commonly use to keep movies out of competing locations.

AMC, which has faced the most backlash in the exhibition industry over the practices, told investors the Justice Department wants information “in connection with an investigation,” according to an AMC notice...