Odom fell on his left arm during the fourth quarter of the Lakers' 99-95 win in Phoenix on Wednesday after getting his legs tangled up with the Suns' Mickael Pietrus after a layup attempt. The injury was diagnosed as an ulner nerve contusion (bruised funny bone), and Odom stayed in the game after getting his arm examined during a timeout following the fall.
At Thursday's practice, Odom received treatment on his arm rather than play on the court.
"Lamar [underwent] work on his shoulder which was a residual effect from last night's fall," Lakers head coach Phil Jackson said. "He fell on his elbow but his shoulder took the blow."
The left-hander is expected to play in Friday's game against the New Orleans Hornets, according to a team spokesman.
"I think he'll be able to play, it's not something that will probably keep him out of playing but it's a problematic kind of thing that's probably going to be affecting him for a while," Jackson said.
Odom appeared fatigued and revealed he didn't fall asleep until 4:30 a.m. after the team's charter flight from Phoenix arrived back in L.A. well past midnight.
"It comes along with the territory," Odom said. "It's sore today."
Odom said he would ice the shoulder Thursday night and intends on playing against the Hornets.
"I'll try," Odom said. "I'm going to have to play right handed. That would be kind of crazy. I don't know how I'm going to pull that one off, but I'm going to try. It's kind of like a sprained ankle ... It's stiff. It's painful. It hurts."
The 12-year veteran is averaging 15.6 points and is ranked 10th in the NBA in rebounds per game (9.5) and third in the league in field goal percentage (57.0) this season.
Odom's left shoulder has caused him problems in the past. He aggravated it last season in a game against the Boston Celtics after hanging on the rim following a dunk but played through it, appearing in all 82 regular season games for the Lakers.
Dave McMenamin covers the Lakers for ESPNLosAngeles.com. Follow him on Twitter. Andy Kamenetzky of the Land O' Lakers blog contributed to this report.