The Buffalo Sabres defeated the Devils 7-1 on Monday night, dropping New Jersey's record to 9-13-4 ahead of Tuesday's game against the Vegas Golden Knights.
Hynes was in his fifth season behind New Jersey's bench. During that span, the Devils went 150-159-45 and missed the playoffs in all but one campaign, in which the Tampa Bay Lightning knocked them out of the first round in five games.
However, the Devils stumbled out of the gate, losing their first six games and nine of their first 11 contests to start the season.
The New Jersey job was Hynes' first as an NHL head coach.