The news was first reported by NFL Network.
It was not immediately clear how long Fuller would be out, but any absence would deprive the Chiefs of their top cornerback.
If the Chiefs go with candidates on their roster for their third cornerback, they can choose from either of two rookies, Tremon Smith and Charvarius Ward. Smith is the Chiefs' sixth-round draft pick and has played just 15 snaps on defense this season. The Chiefs acquired Ward in a preseason trade with the Dallas Cowboys.
Ward joined the Cowboys as an undrafted free agent. Like Smith, he has mainly played on special teams. He has been in the lineup for 10 defensive plays.
Neither played in Thursday night's game against the Los Angeles Chargers.
Fuller played all 74 snaps against the Chargers. He has two interceptions this season, including one shortly before halftime against the Chargers.
Fuller was acquired last winter as part of the trade that sent quarterback Alex Smith to Washington.