Mahomes, who is in his sixth NFL season, appeared to suffer the injury late in the second quarter when Bears defensive end Yannick Ngakoue rolled on his foot.
Mahomes suffered a sprained right ankle that hindered him through the 2022 playoffs. He and the Chiefs went on to win Super Bowl LVII over the Philadelphia Eagles.
Kansas City is 2-1 this season.
Mahomes on Sunday completed 24-of-33 passes for 272 yards and three touchdowns. He also had three carries for 28 yards.
Mahomes won MVP this past season and through three games has thrown for 803 yards, seven touchdowns and two interceptions.
The Chiefs are looking to win their third Super Bowl title in five years. They lost their season-opener against the Detroit Lions but responded with wins over the Jacksonville Jaguars and Bears.
Sunday, Kansas City had a surprise appearance from pop singer Taylor Swift, who is all but confirmed to be dating Chiefs tight end Travis Kelce. Swift was in a suite with Kelce's mother, Donna, and cheered him on.
Mahomes told FOX's Erin Andrews after the game he felt pressure to get Kelce a touchdown in front of Swift. Kelce had seven receptions for 69 yards and a third-quarter touchdown.
“I felt a little bit of pressure, and so I knew I had it get it to Trav… I think he wanted to get in the end zone just as much as all the Swifties wanted him to.”