He sat out two games and returned Nov. 28, when he scored a season-high 25 points against Phoenix.
Billups aggravated the injury when he was hit during Denver's win in Toronto on Friday night. He was evaluated by a team doctor and a hand specialist Tuesday. He's listed as day-to-day.
Billups is averaging 14.4 points and 5.4 assists in 21 games this season.