Billups, who was averaging 14.9 points, 4.0 assists and 2.5 rebounds this season, tore his left Achilles tendon Monday in a game against Orlando.
The 35-year-old guard collapsed to the floor while attempting a crossover move with 5:48 left in the fourth quarter of the Clippers' overtime victory.
Team officials said the tendon tear was found during a magnetic resonance imaging exam Tuesday at the Cleveland Clinic.
He was sent back to Los Angeles for further examination.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged