A Chinese consumer-protection group said Tuesday it is investigating complaints that some Apple Inc. iPhones are spontaneously shutting off even when half their battery life remains.

The problem, which reportedly affects iPhone 6 and iPhone 6s devices, is the latest challenge for Apple in China, where sales have slowed and it has brushed up against a more assertive government. The announcement also comes amid growing concerns about U.S.-China relations after the election of Donald Trump, who has described China as a currency...