Cousins suffered a sprained left ankle late in Sacramento's 121-117 loss to the Memphis Grizzlies on Saturday night. The injury forced him from the game.
Cousins, who was recently named to his second All-Star Game, had to be helped off the court and seemed unable to put weight on the foot. X-rays on the ankle were negative, according to the team.
The Kings big man is in the midst of a career season, averaging a career-high 27.0 points per game to go with 11.3 rebounds.
Kings shooting guard Ben McLemore also is out because of a sprained right wrist.