Rask, 25, was injured while slicing food. He underwent surgery on his right fourth and fifth fingers.
Rask had 14 goals and 17 assists in 71 games last season. His 2017-18 campaign was cut short in March by a shoulder injury.
The Hurricanes opened training camp Thursday, a day earlier than originally planned due to Hurricane Florence. They plan to cancel practice Friday or Saturday depending on the storm.