Millsap already has sat out five consecutive games due to the issue. He was diagnosed with synovitis in the knee when he visited Dr. James Andrews on Monday in Pensacola, Fla.
Millsap, who averages 18.1 points and 7.7 rebounds, will be re-evaluated after sitting out the three games.
The Hawks have struggled without Millsap, losing seven consecutive games entering a Tuesday game against the Phoenix Suns.
Swingman Kent Bazemore (knee) will miss his fifth straight game, and forward Thabo Sefolosha (groin) will sit out for the second game in a row.
"At this point, it doesn't matter who's out on the floor," Atlanta center Dwight Howard said. "The guys who step on the floor have to get the job done."