BEIJING—Chinese exports fell sharply last month owing to weak demand in many major markets, and the government and economists are bracing for further difficulties this year given the prospect of a more protectionist Trump administration.

Exports slipped 6.1% in December from a year earlier compared with a 0.1% gain in November, China’s customs administration said Friday. December’s decline was steeper than the drop of 3% that was the median estimate of 11 economists polled by The Wall Street Journal. It also made December...