A source told ESPN's Adam Schefter that Edmonds has a high ankle sprain and is expected to miss multiple games.
"I don't think he'll make it back in time for this game," Kingsbury said. "And we'll take it from there."
The injury happened on the first offensive play of Arizona's 31-17 win against the San Francisco 49ers on Sunday. Edmonds ran for 3 yards and then limped off the field. He did not re-enter the game. Tests Monday confirmed the severity of the sprain.
Losing Edmonds for at least a game is another blow to an already injury-riddled team, especially in the backfield. The Cardinals have been without running back Jonathan Ward, who suffered a concussion on a scary collision against the Green Bay Packers on Oct. 28. Arizona will monitor Ward's progress this week and decide if it needs to bring in another back. The Cardinals have James Conner, who ran for 96 yards and had another 91 receiving yards Sunday, as the primary running back, who will be complemented by Eno Benjamin. Arizona also has Tavien Feaster on the practice squad as an option.
Edmonds, who has 430 rushing yards on the season with one touchdown, was splitting time with Conner. With Edmonds out, Conner stepped up with a career night, scoring three touchdowns, including one on a 45-yard catch -- the longest of his career. According to the Elias Sports Bureau data, Conner became just the fourth player with 11 scrimmage touchdowns through his first nine games with a team since 1990, joining Randy Moss, Terrell Owens and Fred Taylor. Conner leads the NFL with 11 touchdowns this season.
Beyond Edmonds, the Cardinals are facing a battle of attrition.
Kingsbury wasn't sure if either of his three offensive stars who missed Sunday's game will be back this week against Carolina.
He "didn't have a feel" on the status of quarterback Kyler Murray, who missed Sunday's win over the 49ers with a sprained left ankle, as of "yet."
"I like the way he progressed through the week," Kingsbury said. "He definitely improved. We'll have to see how he looks when we get back out there on Wednesday. Hopefully he can operate and function and do his deal. I really don't have a feel for it right now."
Wide receiver DeAndre Hopkins, who missed the third game of his career Sunday because of a hamstring injury, is still day-to-day, Kingsbury said. Fellow receiver A.J. Green is still in the COVID-19 protocols and will have to test out of it before he can return. He needs to turn in two negative tests 24 hours apart.
"Hoping to get him back sooner than later," Kingsbury said.
Kingsbury said left guard Justin Pugh will be day-to-day with a calf injury that caused him to leave Sunday's game and that right guard Max Garcia "kind of battled through" an Achilles injury Sunday that caused him to leave the game, as well.
Long-snapper Aaron Brewer will likely miss a couple of weeks because of an undisclosed injury, Kingsbury said. Kingsbury and the Cardinals staff don't allow themselves to talk about the number of injuries piling up for an 8-1 team that owns the best record in the NFL.
"You look around the league, and everybody's dealing with it, Kingsbury said. "It's a battle of attrition once you hit the second part of the season, and what you've got is what you've got. You've just got to find a way, and that's been our approach. That's how we talk in those terms as a staff, and our guys responded to it."