Witt will begin serving his ban Saturday against Buffalo and will lose more than $74,000 in salary. He can return March 10 at Toronto.
Witt hit Hagman at 2:21 of the third period on Thursday night. Hagman was injured and did not return to the game, which was won by the visiting Leafs in a shootout. Officials gave Witt a major penalty and a game misconduct.
"We are disappointed to lose a player of Brendan's caliber and character for this period of time, but we understand the League's concerns regarding hits to the head," Islanders general manager Garth Snow said in a statement.
He will also miss games against Colorado, the New York Rangers, New Jersey and Phoenix.