WASHINGTON—The Supreme Court on Monday dodged the question of how far legislative majorities can go to entrench their power by drawing favorable electoral districts, dealing a blow to political minorities who say that partisan gerrymanders deprive them of fair representation.

The court’s unanimous action throws the issue, with its potential to reshape the nation’s political landscape, back to lower courts and future dockets, leaving unclear whether a question that has percolated for decades will be answered ahead of the next...