Hill missed practice Monday in order to undergo an MRI on the joint, which revealed the injury.
The 26-year-old Hill missed the team flight to Dallas for the first leg of the Lakers' three-game road trip against the Mavericks, Houston Rockets and New Orleans Pelicans this week, but will fly commercial to meet the team in Dallas on Monday night.
He is available to play in Tuesday's game against the Mavericks.
Hill is averaging 6.3 points and 6.0 rebounds on the season and pulled down a crucial offensive rebound late in the Lakers' 105-103 victory over Atlanta on Sunday, which led to two game-winning free throws for Pau Gasol.
Despite playing just 14.0 minutes per game, Hill is leading the league so far this season with a 73.3 field-goal percentage (11-for-15) and also is tops in the NBA in offensive rebound percentage at 23.3 percent.
Lakers coach Mike D'Antoni said that Hill has earned a bigger spot in L.A.'s deep 11-man rotation based on his early play, but prefers to not ride him too much.
"Jordan is kind of a spurt guy," D'Antoni said after practice Monday. "The longer the minutes, the [more tired] he gets, the less productive. So he spurts out there and he gives us some energy and he doing a great job. There's no doubt we're trying to find him a few more minutes here and there, but we're trying to be strategic about how his minutes are going to impact the game and they have so far."