Donaldson hasn't appeared in a game since he suffered the injury on July 31.
The veteran slugger was off to a slow start at the plate this season batting .182/.296/.318 with one home run over seven games.
The Twins signed the three-time All-Star to a four-year, $92-million deal with a $16-million team option for 2024 this past offseason.
After an injury-plagued 2018 split between the Toronto Blue Jays and Cleveland Indians, Donaldson had a resurgent and healthy 2019. He hit .259/.379/.521 with 37 homers in his lone season with the Atlanta Braves.
Right-hander Jake Odorizzi will take Donaldson's roster spot when he's reinstated ahead of Saturday's start, according to Phil Miller of the Star Tribune.