The Super Bowl-winning NFL star, 34, who has been dating singer Taylor Swift, also 34, since last summer, shanked a series of shots into the crowd at Lake Tahoe - one of which left a woman in her 20s needing medical attention. He also hit a man on the arm with another ball - and ended up kissing both their arms to apologise.
Video of the incident involving the woman showed police officers comforting the injured sports fan, and People reported an eyewitness said the sports fan was left with streaks of blood in her blonde hair after the blow.
Travis then walked into the crowd to check on her and kissed her on the arm.
The incident happened on the 16th hole when Travis' ball strayed as he played alongside Buffalo Bills quarter back Josh Allen, 28, actor Don Cheadle, 59, and 43-year-old WWE hero The Miz.
It sparked a flood of jokes from Travis' fans, once of whom said on social media: "He can hit me with a golf ball anytime."
Another said on X: "Goal for next year... position myself so that I can be hit by Travis' golf ball," while one more joked: "How good can Travis possibly be at golf if he's hitting fans in the first place?"
On the first hole of the celebrity tournament, a Travis shot struck a man on the arm.
A video posted on X showed him marching down the course with a sheriff before locating the fan who got hit - then shaking his hand and leaning in to kiss his arm as fans at the Edgewood Tahoe Resort laughed and cheered.
Travis later joked taking a picture with the woman he struck was the least he could do.
His brother Jason Kelce, 36, was also playing in the tournament and checked on the spectator, who reportedly said she was unsure which of the Kelces hit the bad shot.
She was able to stand on her own after several minutes of sitting on the ground and staff transported her off the course before play resumed.