The injury doesn't sound serious for the 6-foot-6, 265-pound defensive end, who is expected to be ready to participate when training camp begins at the end of July.
The Saints traded the 27th and 147th overall picks in the 2018 NFL Draft along with next year's first-round selection in order to take Davenport with the 14th overall pick.
New Orleans is looking for Davenport to provide a jolt to an improving defense that ranked 18th in pass defense and seventh in sacks last season.
"He's an athletic guy. That's what you saw at the combine, in college," defensive line coach Ryan Nielsen told The New Orleans Advocate. "He's the got the length and the size. It's exciting to work with him. I think he's done a good job of playing hard and really focusing on the fundamentals and technique just to improve his overall game in the run and the pass. We're working on a couple different rushes that he can master and go to during the game."
Davenport totaled 186 tackles, 22 sacks, 38 tackles for loss, six forced fumbles, two fumble recoveries and eight passes defensed during 43 games at Texas-San Antonio.
He was named the Conference USA Defensive Player of the Year in 2017 after logging 55 tackles, including 17.5 for loss, 8.5 sacks and eight quarterback hurries.