The Kings said before the game that Cousins would sit out. He also missed Sacramento's 112-104 loss at San Antonio on Friday night with the illness.
Ryan Hollins is expected to make his second straight start at center in Cousins' place. Cousins leads the Kings with an average of 23.5 points and 12.6 rebounds.
The Kings also said Rudy Gay (right achilles tendinitis), Darren Collison (bruised left quadriceps) and Ramon Sessions (right knee strain) are probable to play against Memphis with minor injuries.