Henson hurt his left ankle in a Dec. 20 game against Cleveland and subsequently missed the Bucks' Saturday loss to Minnesota.
Drew said the 6-foot-11 second-year player out of North Carolina will also miss the team's upcoming three-game Western Conference road trip.
Henson has played a big role this season for the Bucks, who selected him 14th overall in the 2012 NBA Draft, averaging 12.4 points and a team-high 8.0 rebounds per game.
He ranks fifth in the league with 2.25 blocks per contest.
Larry Sanders, newly recovered from a broken thumb, will start in Henson's absence.