The Houston Texans selected the outside linebacker with the first pick in last month's Draft, but he developed a groin problem during the team's mini-camp.
The 21-year-old told ESPN: "The pain, the injury's getting better every day, day by day. Just looking forward to getting healthy and looking forward to training camp.
"Just when I got here, they wanted to check me out and I told them there was a little pain. They were like we just don't want it to linger over into the season, so we got it taken care of before anything happened."
Clowney is expected to recover from the procedure in time for the start of the team's pre-season training camp next month.