Anthony, who has missed Denver's last three games with a right knee contusion, worked out before the game but ruled himself out.
Nuggets coach George Karl said backup point guard Ty Lawson will likely sit out with a sprained left ankle, while Nene (sprained right ankle) and Chris Andersen (sprained left ankle) will most likely play.
Billups, the team's second leading scorer, missed eight of the last nine games and the last five with a strained left groin muscle.