Johnson got the start in Game 3 of the Eastern Conference Finals but only scored two points in nine minutes as the Celtics earned their first win of the series.
After averaging 6.5 points and 4.6 rebounds per game during the regular season while starting 77 of 80 games, he has been almost a non-factor in the playoffs with just 2.7 PPG.
He has just four total points scored in 26 minutes this series, and was minus-15 on the court in the team's recent win.
Gerald Green has earned a handful of starts during the playoffs, but Jonas Jerebko could be a candidate for more playing time after a breakout appearance Sunday. He finished with 10 points and five rebounds while ending plus-22 on the court.
Jaylen Brown and Kelly Olynyk should also get more minutes if Johnson is unavailable.
Game 4 is scheduled for Tuesday at 8:30 p.m. ET with the Cavaliers holding a 2-1 series lead.