Johnson injured his shoulder in the opening minutes of Sunday's Game 3 when he got tangled with Cleveland's Tristan Thompson while chasing a rebound. Johnson later returned to the game but did not practice on Monday.
Celtics coach Brad Stevens said Tuesday morning that Johnson would go through shootaround and the team would determine his status for Game 4.
Even as a starter, Johnson's playing time has been limited this postseason. Johnson is averaging 2.7 points and 2.1 rebounds over 10.5 minutes per game in 13 appearances, including nine starts.