The 19-year-old did not travel with the Bruins to Montreal, where they will play the Canadiens on Tuesday night.
In their statement, Kessel's family did not specify what he was being treated for and offered no update on his condition. They also asked for privacy on the matter.
Kessel has five goals and nine points while appearing in all 27 Bruins games this season. He last played in Boston's 5-1 loss to New Jersey on Saturday night.
The Bruins recalled centre Yan Stastny and goaltender Hannu Toivonen from Providence of the AHL.