Bears head coach Matt Nagy confirmed the surgery to reporters Monday at Halas Hall, adding that the procedure "went well."
"We're staying optimistic for Green Bay," Nagy said, expressing hope that Floyd would be on the field for the Bears' regular-season opener against the rival Packers.
Nagy described the fracture as on Floyd's index and middle finger. It occurred on a cut block late in the first quarter of the Bears' preseason game against the Broncos; Floyd hit the ground and injured his hand as he braced himself.
"[He was] just unlucky," Nagy said.
"I talked to him," Bears defensive end Roy Robertson-Harris added. "I think Leonard's going to be fine. He's going to come back and rush his butt off."
Floyd, the ninth overall pick in the 2016 draft, has played only 22 combined games in the past two seasons due to injuries.
With three weeks to go before the start of the regular seaso, the Bears are testing their depth at the outside linebacker position. Floyd's backup Aaron Lynch has a hamstring injury and hasn't played in the preseason. The other backups at the position are Kasim Edebali, Kylie Fitts and Isaiah Irving.