Ingram suffered the injury on Thursday against Miami and underwent an MRI on Sunday. The Lakers say the forward will be re-evaluated in about a week.
Ingram said the injury to his left groin is in the same spot as a previous injury.
"I'm just happy it is not as [bad] as it could be [potentially]," Ingram said. "I was hit directly in the spot that I have had problems with before but it wasn't as [bad] as it is right now. It is something that I will get through."
The Lakers play Portland, Orlando and at Denver this week.
Head coach Luke Walton did not rule out Ingram returning to play the Cavaliers next Sunday.
"But it depends on how his body recovers," Walton said. "He has done a lot for us, it is not just his scoring that we will miss. He has been a huge piece in the success we have had recently in playing the point guard position, playmaking, really stepping up in the way he rebounds the ball, using his length to get in there and help us finish off defensive possessions. His versatility, the amount of positions he can guard, there is a lot that we are trying to figure out a way to fill in for without him out there."
Ingram missed the Lakers' last game at San Antonio on Saturday.
Kyle Kuzma started that win in place of Ingram. The Lakers have lost two starters to injuries in the past week, with rookie Josh Hart expected to be out four to six weeks after undergoing surgery to repair a fractured fourth left metacarpal.