A source told ESPN's Adam Schefter that Penny "would have played with it if this were late season/playoffs."
Carroll said the injury happened during a pass-blocking drill on Monday and that Penny will need a couple of weeks to recover.
"He had a surgery that worked out beautifully. It's a couple weeks [that he will be out]," Carroll said. "He can already move it, and he's not going to be in a cast or any of that kind of stuff. So he's in pretty good shape. ... He's not going to be out very long at all."
The Seahawks open the season against the Denver Broncos on Sept. 9.
The Seattle Times was first to report the specifics of Penny's injury.
Penny was selected 27th overall in this year's draft. He had been competing with Chris Carson for Seattle's starting running back job.
Carroll said running back depth was a "little bit" of a concern Wednesday. Mike Davis missed practice with a toe injury, while C.J. Prosise, returned to practice following a hip injury and will try to play in the team's preseason game Saturday.
"We felt it today," Carroll said. "... At this point, we're OK. We're in good shape."
In 2017, his first season as a full-time starter at San Diego State, Penny led the nation with 2,248 rushing yards to go along with 23 rushing touchdowns, which ranked second.
ESPN's Brady Henderson contributed to this report.