According to Shams Charania of The Vertical, the forward is expected to miss "extended time" due to a left knee problem.
Morris has been in and out of the lineup in recent weeks, missing Sunday's game due to the injury.
The Celtics acquired Morris in July from the Detroit Pistons to clear cap space so they could sign free agent Gordon Hayward. Even though Hayward's season ended in the first quarter of the season opener against the Cleveland Cavaliers, Boston has thrived with a 17-game winning streak after an 0-2 start.
The squad still has the best record in the NBA with a 23-5 record.
Morris has been a terrific addition to the Celtics. The 28-year-old is averaging 12.1 points with a career-high 5.5 rebounds per game.
With Morris on the shelf, Boston will likely rely upon more minutes from Aron Baynes and Daniel Theis at power forward. Guerschon Yabusele is also on the roster and can get some run until Morris is able to return.