According to NFL Network's Mike Garafolo and Ian Rapoport, the surgery was described as a "cleanup," and he is expected back in time for the start of training camp.
The 29-year-old reached his fourth straight Pro Bowl in 2018 after he racked up career highs with 103 receptions for 1,336 yards and 10 touchdowns. He was also named a First Team All-Pro for the second time.
Kelce has topped 1,000 yards in each of the past three seasons, and he has never finished with fewer than 862.
Injuries generally haven't been a problem for Kelce. A knee issue landed him on injured reserve after one game as a rookie in 2013. Since then, he has missed just one contest.
Kelce has been one of Kansas City's vital offensive players for a few years, and he, along with wide receiver Tyreek Hill and quarterback Patrick Mahomes, gives the Chiefs one of the NFL's most potent offenses.
Provided Kelce heals as expected, the Chiefs will once again be among the NFL's top Super Bowl contenders in 2019 after they made it to overtime of the AFC Championship Game last season.