Parker crumpled to the court with a sprained left ankle during the third quarter and needed assistance in order to leave the floor.
The injury came as San Antonio was winning for the 18th time in 21 games. The Spurs bounced back from a four-point loss to Phoenix on Wednesday that ended their 18-game home winning streak.
DeJuan Blair led a balanced San Antonio attack with 16 points. Danny Green had 15 points, Manu Ginobili had a career-best 15 assists and Parker contributed 13 points with seven assists before the injury.
The Spurs shot 60 percent from the floor and made 9-of-20 from 3-point range.
Marcus Thornton scored 25 for the Kings, who have lost seven out of eight.