Undav, who pulled out of Germany's Nations League fixtures this month, suffered the injury on Wednesday, with a scan confirming a muscle tear.
"We'd be doing well if we see him on the pitch again this year," Hoeness told reporters while not entirely ruling out his return before the winter break.
Undav, 28, hurt his hamstring in the Champions League defeat by Atalanta two weeks ago and missed Stuttgart's next game, a 3-2 loss against Eintracht Frankfurt.
Hoeness said Undav, who has five goals in nine league games this season, had reinjured "the same muscle".
Undav is the latest addition to a lengthy injury list for last season's runners-up that includes Jamie Leweling, El Bilal Toure, Dan-Axel Zagadou and Luca Raimund.
Hoeness said it would be "tight" for Undav's Germany teammate Angelo Stiller to return from a muscle injury in time to face Bochum on Saturday, while Ameen Al-Dakhil and Anrie Chase are also in doubt.
