"He has a mild sprain PCL (posterior cruciate ligament)," coach Bruce Arians said. "There's no timetable. It could be a week, could be three weeks. He's a tough guy, we know that, played last year with a lot worse."
Arians wouldn't rule Ellington out for Sunday's game at Chicago.
Ellington played all of last season with a torn tendon in his left foot. He was hurt on Sunday, Arians said, when his knee slammed into the ground on a 16-yard run early in the fourth quarter.
The Cardinals rushed for 120 yards against the Saints, averaging 4.8 yards per carry. Last season, their average of 3.3 yards per attempt ranked last in the NFL.
Arians was pleased with the running game Sunday, but it could have been better.
"We left a lot of yards out there, though," he said. "It should have easily been 150 yards."
Ellington gained 69 yards in 12 attempts. Chris Johnson carried 10 times for 37 yards.
Chris Johnson, a three-time Pro Bowl player early in his career, was signed late in training camp and still is getting accustomed to Arians' offense.
"I'm getting there," Johnson said on Monday. "Just working, just having to learn the playbook and not having to think about the plays, just going out there and playing. The more and more I practice and I know the more and more I play, I'll get there."
David Johnson, a third-round pick out of Northern Iowa, touched the ball twice on Sunday — returning a kickoff 43 yards before his big touchdown catch.
On that play, he took a short toss from Palmer, then turned the corner and burst away from the defense down the sideline to score with 1:33 to play.
Arians, as is often the case, went against conventional wisdom and called a pass play with his team ahead when most would have kept it on the ground to try to run out the clock.
"The same way I play golf," he said. "I don't lay up. I've hit a lot of balls in the water but you can't hit a great shot if you don't try."
Asked if he envisioned an expanded role for David Johnson, Arians said, "in time."
"I don't want to put too much pressure or take rookies and give them too much a piece of the pie too early," the coach said. "It's not healthy to put them in the situation too much."
Palmer, in his first game back after tearing an ACL last season, threw for three touchdowns, completing 19 of 32 passes for 307 yards with no interceptions.
Drew Brees threw for 355 yards, but the Cardinals' defense stiffened in the red zone, allowing only one touchdown in four New Orleans trips inside the 20.
Arizona had big problems defending screen and swing passes out of the backfield.
Arians said outside pass rushers weren't peeling back to defend the running back.
Safety Rashad Johnson said that aspect of the defense must improve in a hurry.
"I think (the Bears') Matt Forte is the best at it when it comes to the screen game," Johnson said. "He's an elite back. He can do it all."