Denver coach George Karl said Afflalo was hurt late in the Nuggets' 108-104 victory at Washington on Friday. Andre Miller started in his place.
Afflalo likely would have spent some time defending Carmelo Anthony, whom he often worked against in practice before the Nuggets traded Anthony to the Knicks last February.
Nene didn't play at Washington because of a left heel strain.
Reserve guard Rudy Fernandez also was expected to sit out because of a right Achilles' tendon strain.