The team announced Hayward had surgery to repair a fourth metacarpal fracture in his left hand. He is expected to return to play in about six weeks, according to the team.
Hayward suffered the injury in Saturday's 135-115 victory over the San Antonio Spurs.
The former Utah Jazz star fractured his hand when he collided with Spurs forward LaMarcus Aldridge, who was whistled for an illegal screen on the play. Hayward failed to see the screen and his left arm got caught between his body and Aldridge's.
Hayward immediately grabbed his hand and went to the Celtics' locker room. The team later announced that X-rays confirmed the fracture and ruled him out for the game.
Hayward, who scored nine points in 15 minutes against the Spurs, is averaging 18.9 points, 7.1 rebounds and 4.1 assists through eight games this season. He is shooting 55.5 percent from the field, including 43.3 percent from 3-point territory.
The Celtics hosted the Dallas Mavericks on Monday night.