The Devils' GM didn't disclose the exact nature of Kovalchuk's injury, but did say an X-ray revealed there would be no need for surgery.
The left wing was hurt Saturday during team's 2-1 win over Florida when he fell awkwardly into the end boards while trying to avoid a check. He skated off under his own power but was clutching his shoulder.
Kovalchuk is New Jersey's second-leading scorer with 27 points, including 10 goals and 17 assists.
Fighting for an Eastern Conference playoff spot, the Devils also announced that previously injured forward Alexei Ponikarovsky had been placed on injured reserve.
Ponikarovsky sustained a lower-body injury March 19 after arriving from Winnipeg. He has provided just one goal and five points over 17 games this season.