Brodeur, who is 13-19-2 with a 2.74 goals-against average, injured his knee during the first period of Sunday's 4-1 win against the Montreal Canadiens and was replaced at the start of the second period by backup Johan Hedberg.
He underwent an MRI exam Monday, which revealed that he doesn't need surgery.
"We don't know [how long he's going to be out]," Devils general manager Lou Lamoriello said. "It's non-operable. He's going to undergo rehab and physical therapy. When he feels good, that's when we'll know he's OK."
Lamoriello said he was relieved the injury wasn't more serious.
"I went into a butterfly and my leg got caught up under me and I kind of heard a click," Brodeur said after the game. He watched the third period in Lamoriello's box. "[Monday] we'll see how it feels. I don't think it's anything major."
The Devils called up Mike McKenna from Albany of the AHL Tuesday to back up Hedberg.
"I am just going to try to play it game by game," said Hedberg, who entered Tuesday 6-10-2 this season.
The Devils, who have had the worst record in the NHL most of the season, entered Tuesday with a 9-1-2 mark since Jan. 9. Brodeur has gone 8-1-1 in that span.
"It's tough with Marty, but Moose [Hedberg] has been playing pretty good for us," center Travis Zajac said, "so we are going to have to lean on him while Marty is hurt."
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from The Associated Press was used in this report.