Coach Gary Kubiak said the finger was broken Wednesday after being hit with a ball. He said it was a compound fracture, meaning the bone broke through the skin.
Reeves was released from the hospital Thursday after having a procedure to repair the finger.
This is the second broken bone this season for Reeves, a starter last year, who broke his leg early in camp and hasn't played this season.
He expects to return next week.
"It's a pinky, man, I'll be all right," he said. "I have a pretty high pain tolerance so I should be all right."