Brown is the latest Celtics player to battle a hip ailment.
Isaiah Thomas was shut down for the season after aggravating a lingering hip injury in Game 2 of the series. Avery Bradley has battled through hip pointers on each side of his body since the Washington series in Round 2.
Crowder, who fell awkwardly during the second half, deemed himself "fine" after Tuesday's Game 4 loss while Johnson was active despite being pulled from the starting lineup because of soreness in his shoulder since he was tangled with Tristan Thompson in Boston's Game 3 win.
The Celtics started Kelly Olynyk at center in place of Johnson on Tuesday. The Cavaliers lead the best-of-seven series 3-1.
Brown talked to reporters after Tuesday's game and did not allude to an injury. The rookie swingman is averaging 4.9 points and 2.3 rebounds over 12.9 minutes per game in 16 appearances this postseason.