The league rejected the 17-year deal contract last week, saying the longest contract in league history violated its salary cap.
The union disputed that belief in its grievance Monday. It said that under the collective bargaining agreement, the union and Kovalchuk are entitled to an expedited resolution.
The NHL acknowledged that it has received a copy of the grievance.
"Although there is no defined timetable at this point, we intend to work with the Players' Association to ensure an expeditious resolution of this dispute," NHL deputy commissioner Bill Daly said in a statement. "The league looks forward to the opportunity to establish its position before the arbitrator."
Daly said that the league would have not further comment until the issue was resolved.
Kovalchuk's deal was likely rejected because he was to earn $550,000 in each of the last five seasons of the contract that was to run through the 2026-27 season, when he would be 44. He was to earn $98.5 million in the first 11 years of the deal.
By extending Kovalchuk's contract and paying him less money late in the deal, the Devils lowered their salary-cap hit to $6 million annually.
Devils president and general manager Lou Lamoriello said last week that he believed that the contract complied with the terms of the collective bargaining agreement. He also said he would not comment again until the grievance process played out.
Kovalchuk's agent, Jay Grossman, also said last week that he wouldn't comment until the matter is resolved.