Jagr, who played all 82 regular-season games, was hurt Saturday just moments before Patrik Elias' power-play goal gave New Jersey a 6-1 lead with only 4:26 remaining.
The Rangers were also without defenseman Darius Kasparaitis, who aggravated a groin injury during Monday's skate before Game 2 of the first-round series. Kasparaitis was shelved for 12 of the final 14 regular-season games.
"He felt really uncomfortable so we decided not to dress him," coach Tom Renney said.
Very rarely during the season was Jagr used to kill penalties. Renney was criticized for changing that policy so late in a playoff blowout.
New York allowed five goals in 13 shorthanded situations against New Jersey, and Renney backed up his decision to play Jagr by saying he could use practice killing penalties.
Jagr was injured when he tried to stiff-arm Devils forward Scott Gomez while carrying the puck.
Renney said Jagr felt better on Monday after receiving treatment and expected that he would play again during the series.
"Whether it means Wednesday or Saturday, I'm not sure," Renney said. "He feels good that it's improving. If he feels good, so do we."
The Rangers, who dropped their final five games of the regular season to fall from first to third in the Atlantic Division, were already big underdogs to the surging Devils before losing their biggest offensive force.
Jagr finished with team records of 54 goals and 123 points and led the NHL in both categories for much of the season. Renney had no option even close to that to replace Jagr. Petr Sykora was expected to move up from the second line to fill in with Michael Nylander and Martin Straka.
Chad Wiseman and Colton Orr were inserted into the lineup for Jagr and fellow right winger Jason Ward, who was lost for at least this series on Saturday when he sprained a knee ligament just 6:39 in. Wiseman was recalled from AHL Hartford on Sunday.
Ward was one of the Rangers' penalty-killers this season, so not having him could prove costly if New York continues its undisciplined play and is forced into more short-handed situations.
Jason Strudwick took Kasparaitis' place in the lineup.
New Jersey went without Colin White but his absence could've been more costly if Jagr was playing. The defenseman has been used by Devils coach Lou Lamoriello as part of a five-man checking crew against Jagr and the Rangers' top line.
White injured his groin late in the season and was only 50-50 to play in the series opener. He gave it a try but aggravated it in the first period and didn't return. David Hale, who played 38 NHL games this season, dressed as New Jersey's sixth defenseman.