Millsap will miss Wednesday night's game against the Chicago Bulls. The Hawks say Millsap also will be held out on Thursday at Boston.
The Hawks say center Pero Antic, who has missed the past 14 games due to a stress fracture in his right ankle, also will be held out against the Bulls and Celtics. Center Gustavo Ayon will miss his fourth straight game against the Bulls with a right shoulder injury.
Antic and Ayon were the replacements for Al Horford, who is recovering from season-ending surgery for his torn right pectoral muscle.
The Hawks ended an eight-game losing streak by beating the Knicks on Saturday night.
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