Kovalchuk had two goals and three assists in the Devils' first seven games.
Kovalchuk signed a controversial 17-year, $102 million contract in the offseason that the NHL said circumvented its salary-cap rules. The Russian eventually signed a revamped 15-year, $100 million contract.
The NHL fined the Devils $3 million and took away two high draft picks over the next four years.
New Jersey hosted Buffalo on Saturday night.