Boychuk was injured in the second period of the Islanders' series-clinching win over the Pittsburgh Penguins on Tuesday. He left the game and did not return.
The timeline would knock Boychuk out for at least the team's second-round series. The Islanders, who are in the second round for just the second time in 26 years, will face the winner of the Washington Capitals-Carolina Hurricanes series, which is tied 2-2.
Boychuk tallied three goals and 16 assists during the regular season. He had one assist in the Islanders' four-game sweep of the Penguins.