The Sabres will provide an estimated recovery time later this week.
Cozens, the seventh overall selection last month, hurt his left thumb when defenseman Brandon Hickey hip-checked him during Saturday’s three-on-three tournament inside Harborcenter.
After Cozens, 18, got up from the ice, he removed his glove and examined his thumb, which was bent awkwardly. The center then went to the dressing room and didn’t return.
Later in the day, Cozens kept his hands in the pockets of his hoody while being interviewed. He appeared to be wearing a splint.
Cozens said then his thumb wasn’t broken and he would see a specialist Monday.