BEIJING—A private-sector data provider has quietly stopped publishing a widely watched barometer of China’s property market that was one of the few alternatives to an official gauge, leaving a hole in a government-dominated flow of information on the Chinese economy.

Beijing-based Fang Holdings, China’s largest online real-estate portal, has since at least 2010 published its compilation of home prices in 100 Chinese cities into a monthly index. The index usually shows sharper increases in China’s runaway property prices than...