Kelly, who will have surgery on a bone defect, is expected to be sidelined 6-8 weeks, a source told ESPN's Adam Schefter.
Kelly injured his foot during the Colts' joint practice against the Lions last Thursday. The Colts put Kelly in a walking boot for the past week to immobilize the foot with the hope that it would heal on its own. That wasn't the case, which led to Kelly needing surgery.
"He'll make a complete recovery on it," Pagano said. "He's going to miss some time. How much time? I don't know. I don't have a timetable."
Kelly, the Colts' first-round pick in 2016, started every game during his rookie season.
The Colts will look to add help on the offensive line. They had veteran free agent center/guard Jeremy Zuttah in for a workout last week. Zuttah was a Pro Bowl alternate with the Baltimore Ravens last season.
"We'll look at everybody," Pagano said. "The roster's fluid. We bring guys in all the time."
The Colts are now missing their starting center and quarterback, as Andrew Luck remains on the physically unable to perform list while recovering from offseason shoulder surgery.