The suspension will begin with Friday night's Game 5 clash against the Buffalo Sabres. The Islanders face elimination if they lose. Hill had one goal and 24 assists in 81 games this season, his first with the Islanders.
He did not record a point in the Islanders' first four playoff games against Buffalo.
Hill, a 37-year-old from Duluth, Minn., was drafted by the Montreal Canadiens in the eighth round of the 1988 NHL entry draft.
He signed as an unrestricted free agent with New York in August.
In 841 career regular-season games, Hill has recorded 60 goals and 229 assists for 289 points.