Davis and Smith are the defending NFC champions' top two offensive threats.
Davis, who ran for a career-best 1,444 yards last season, began having problems with his knee after practice Thursday, and an MRI showed "a small cartilage problem," coach John Fox said Friday.
He had arthroscopic surgery Friday, and will miss Sunday's game at Kansas City. The Panthers said he would be out two to five weeks.
Smith, who led Carolina in receptions (88) and yards receiving (1,110), is out indefinitely after breaking his left leg in Monday night's loss to Green Bay.
DeShaun Foster will replace Davis at running back, and rookie Keary Colbert is expected to start at receiver. Chris Gamble, another rookie, could replace Smith on punt returns.
"As I told the team, we have got 53 men out here we think we can start and win for us. They have got to step up," Fox said. "It is part of the game. Kansas City is going to play without some starters. These guys understand that. It is not the first time it has happened."
Foster was a solid backup to Davis last year, and started two games in place of him while Davis nursed an ankle injury. He ran for 429 yards on 113 carries, and had 26 receptions for 207 yards and two touchdowns.
Foster was also solid in the postseason, running for 196 yards and two touchdowns in four games.
He first proved his worth in a regular-season game at Indianapolis, filling in for Davis when he left in the second half with a bruised arm. Foster came in and carried 16 times for 85 yards to help the Panthers to an overtime victory.
But that was behind a drastically different offensive line than Carolina has this year. Three starters are gone from that unit, and the Panthers struggled to run behind the new line on Monday night. They had just 38 yards on the ground, and Davis had 26 on nine carries.
Davis, who set career marks last season for rushing touchdowns (eight), rushing attempts (318) and 100-yard rushing games (seven), said last week that staying healthy was the only goal he set for himself this season. He's completed a 16-game schedule just once in his career, in 2001.
"Being a running back in the NFL, you will get the wear and tear," he said. "You have to be durable to go through it. But that's a goal, to play the whole season injury free, although anything can happen. I'm just going to take it one game at a time and roll on."