The defensive end, who was the first overall pick in this year's Draft, will miss the team's minicamp next week, but is expected to fully recover from the procedure in time for the start of training camp in July.
Head coach Bill O'Brien told reporters: "I don't think it was too long [that he was dealing with the pain].
"I think it wasn't too long, but again you know, we looked at it as let's take care of it now and he will be ready to go for training camp. We're looking forward to seeing him in training camp."
The Texans added Clowney to their roster with the first pick after finishing the 2013 NFL season with the worst record in the league.