James limped out of the Lakers' 114-101 loss to the Los Angeles Clippers with 5:41 remaining in the fourth quarter on Wednesday and told reporters after the game he felt he had strained his groin.
The four-time NBA MVP missed 17 straight games in the 2018-19 season due to a torn left groin.
James underwent an MRI on Thursday, which revealed he did not suffer a tear, but has a left adductor strain.
"It's not torn, that's the biggest thing, that he didn't tear anything," Ham told reporters. "It was good news.
"I'm sure it's painful. Doubtful, day-to-day, whatever - I'm just happy there wasn't anything torn."
The Lakers have struggled to a 2-9 start to the season but James has provided strong output, averaging 24.3 points, 8.9 rebounds and 7.1 assists per game.
The Lakers suffered their fifth straight loss in a game where James has scored 30 or more points against the Clippers on Wednesday.