The heritage-listed building on Orwell Street was set to be converted into a luxury boutique hotel with a 250-seat auditorium by developers Central Element.
The planning proposal drew protests from hundreds of residents, who launched the Metro-Minerva Theatre Action Group to preserve the venue for its original use.
Central Element put the site on the market just weeks after the development was approved to focus on its ultra-luxury residences.
Packer is reported to have bought the site through her company, Sacred Firebird which is co-run with the manager of her family office, Glen Selikowitz.
Potts Point residents celebrated the sale in a local community Facebook group.
"Gretel has answered the call and I feel very comfortable with the building in her hands. She knows the building's history and has a keen interest in the arts," a founding member of the Metro Minerva Theatre Group wrote.
"I look forward to learning more about her vision."
The Metro-Minerva, located in the heart of Sydney's Kings Cross, initially opened as a live theatre before it was converted into the Metro Cinema in the 1950s.
The venue later became home to director George Miller's production company in the late-70s, which made Mad Max, Babe and Happy Feet from the premises.