Smith, a preseason All-ACC receiver, was the team's top target last season, catching 60 passes for 980 yards and seven touchdowns while battling through nagging injuries.
After feeling ill Thursday night, Smith awoke Friday and experienced severe pain before being taken to the hospital, where the emergency surgery was performed.
"We were fortunate to catch this early, and we anticipate a full recovery," Louisville head trainer Matt Summers said.
There's no timeline for Smith's return to the practice field. The Cardinals opened fall camp Friday afternoon.