Martinek, 33, tore the anterior cruciate ligament in his right knee in the third period of Friday's 2-1 loss at New Jersey after being hit hard along the boards.
The defenseman had two goals and an assist in 16 games this season. He had six goals and four assists in 51 games last season.
Meanwhile, Isles captain Doug Weight is expected out for a week with an upper-body injury.
Celebrity Families of 2014 [PHOTOS]