Palmer won't have surgery for about two weeks, Arians said, to allow time for the swelling to subside. Arians expects Palmer to return by late June or early July. There was no damage to other ligaments or tendons in Palmer's knee.
Palmer was placed on season-ending injured reserve Tuesday. The Cardinals signed quarterback Ryan Lindley off the San Diego Chargers' practice squad in a corresponding move. Lindley had spent the last two seasons with the Cardinals after being picked in the sixth round of the 2012 draft.
"It's hard," Arians said. "I knew walking out on the field what I was going to find. You're pulling for a guy because he's put so much into it, to get into the playoffs and win some games and maybe go all the way, because you know what it means to him at this point of his career.
"This team is special and we'll miss him on the field, but his leadership will still be there."
Arians said the Cardinals are looking at signing a third quarterback. After Palmer was injured earlier this season, Arizona signed Dennis Dixon, who played for Arians in Pittsburgh. As of Monday afternoon, the team had not announced any signings.
Palmer, who was on crutches Monday, was injured on a sack by Rams safety Mark Barron early in the fourth quarter of the Cardinals' 31-14 victory Sunday. Palmer stepped up as Barron ran by him, and he said the turf at University of Phoenix Stadium gave. He called it a freak injury.
Palmer said he's stepped out of a blitz like that thousands of times. He said he heard his ACL pop and knew what happened before doctors officially diagnosed the injury.
"Selfishly, very unfortunate," Palmer said. "A bump in the road for me, but I've been through this before and I've had something worse actually before. I'm going to attack this thing. I'm going to grind and be back and hopefully be back here and be ready to roll by OTA time."
Palmer leaving press room on crutches... pic.twitter.com/Z4e7Cfhkky— Josh Weinfuss (@joshweinfuss) November 10, 2014
The injury came just two days after Palmer, 34, signed a three-year contract extension worth a reported $50 million, including $20.5 million guaranteed. He also tore his left ACL in 2006, 10 days after signing a $118 million extension with the Bengals.
The Cardinals have the league's best record at 8-1 and sit atop the NFC West.
"It's not easy," Palmer said. "Not going to lie, I cried like a baby last night. I'm not an emotional guy. I don't cry. The last time I cried like that was when I lost my friend and [Bengals] teammate Chris Henry in '09.
"It's obviously not ideal and not something anybody wants to go through, especially with all the positive and the good going on."
Palmer was 25-for-36 passing for 241 yards and an interception before the injury. He missed three games earlier this season with a damaged nerve in his throwing shoulder. The Cardinals won two of those three games with Drew Stanton starting at quarterback.
Stanton replaced Palmer on Sunday, taking the Cardinals to their fifth straight victory.
In addition, Stanton's wife gave birth to their first daughter on Monday night, a league source told ESPN NFL Insider Adam Schefter.
"As far as our football team, everybody in the locker room including in myself has all the confidence in Drew," Arians said. "You all should too by now."