He is planning on missing two games.
Billups injured the groin on Dec. 16 against Houston and sat out three straight games. The All-Star point guard returned on Christmas Day at Portland, but didn't play in the second half.
The Nuggets said in an injury update report Sunday that the move was "not a setback" and the goal was to avoid a "lingering problem."
The Nuggets travel to Sacramento on Monday. They will then be off for the next four days, before traveling to Utah on Jan. 2.
Billups is averaging 17.1 points and 5.7 assists this season.
Information from The Associated Press contributed to this report.