Antetokounmpo suffered a hyperextended left knee during Game 4 on Tuesday and had been listed as doubtful for Thursday night's game. An MRI showed no structural damage or ligament damage, sources told ESPN's Adrian Wojnarowski and Zach Lowe on Wednesday.
Sources said a timetable for Antetokounmpo's return is unclear.
Milwaukee leads the series 3-2.
Bucks coach Mike Budenholzer said Antetokounmpo did work in the weight room at shootaround Thursday morning but didn't do any on-court work. Antetokounmpo has been averaging 28.2 points, 12.7 rebounds and 5.2 assists in the postseason.
Atlanta Hawks star Trae Young also sat out Thursday night's game because of a bone bruise in his right foot. Center Clint Capela, who was questionable after taking an inadvertent elbow to the face late in Game 4, started in Game 5 and had six points and eight rebounds in 21 minutes.
Antetokounmpo left Game 4 against the Hawks with just over seven minutes remaining in the third quarter after landing awkwardly on his left leg while contesting an alley-oop to Capela from John Collins.
The two-time MVP immediately fell to the floor and stayed down on the ground for several minutes -- with Bucks and Hawks players and coaches surrounding him -- before sitting up and being helped to his feet.
The Bucks haven't indicated how they might adjust their starting lineup without Antetokounmpo. When Antetokounmpo was unavailable during the regular season, the Bucks moved Bobby Portis or Pat Connaughton into the starting lineup.
"It's not something where you ... need to consciously think, 'I need to do more,'" Connaughton said after Thursday's shootaround. "It's just you're ready for opportunities as they arise. Throughout the season, one of the, I would say, beautiful things about our team is you're called to do different things on different nights."
Milwaukee went 6-5 during the regular seasons in games missed by Antetokounmpo.
"We talk about ball movement and people movement and playing free, playing organically," Budenholzer said Wednesday. "We've got a lot of talent, so I think just let the guys play. Put them in a comfort level and put them in a comfortable spot and let them go play basketball, not over-complicated.
"We've played games without Giannis, without Khris [Middleton], without Jrue [Holiday], without whoever it may be, and so hopefully you have a structure and a system where you can function at a high level on both ends of the court no matter who is playing."
ESPN's Malika Andrews and The Associated Press contributed to this report.