Coach Ken Whisenhunt said Sunday the injury doesn't appear serious but it's uncertain how much practice time Arizona's first-round draft pick will miss.
"We'll see how he progresses through the week," Whisenhunt said. "I don't anticipate it will be what everybody's reacting to, saying he's out for a month or something like that."
Wells agreed on a five-year, $11.8 million contract, with $6.3 million guaranteed, on Saturday. He was hurt later in the day when he was carrying the ball in a drill near the end of the workout.
"It was a little pain but I got up and walked off with it," he said. "It wasn't anything too serious. They just wanted to get an MRI and get it checked out."
Wells watched Sunday's practice and afterward acknowledged his frustration.
"I'm definitely disappointed about it," he said. "I've been going through the injury thing quite a while now and yesterday was just a fluke. It could have happened to anybody. Somebody just rolled up on my ankle."
Wells, who missed the first three games of his final season at Ohio State with a foot problem, was grateful this injury wasn't more serious.
"If you guys saw it it was a bad play and I'm just fortunate to walk away from it with nothing but an ankle sprain," he said.
Wells already was behind after missing the team's summer voluntary workouts because his Ohio State classes were still in session.
"I'm still staying caught up with Coach [Curtis] Modkins and the rest of the running backs in the film room," Wells said.
After he arrived Saturday, Wells said it was his goal to win the No. 1 running back job by the start of regular season. Second-year pro Tim Hightower is listed as the starter. Wells said his feelings haven't changed.
"I think an ankle sprain is nothing too major," he said. "If I get on top of it, it will go away quickly."
Whisenhunt downplayed the significance of the injury to Wells' status on the team.
"Unfortunately for Beanie, he's a rookie and it would have been nice to get him some reps," the coach said, "but we still have plenty of time to do that."