The Hollywood Cinema was known for its screenings of the Rocky Horror Picture Show in the 1970s and 1980s and for showing silent movies accompanied by the Wurlitzer.
Grefstad passed away in 2002 and since then the cinema has been owned and managed by his nephew, Mark Matheson, who could not be reached for comment.
Wurlitzer Organ Trust chairman James Duncan said news of the cinema's sale was "devastating".
"We're absolutely reeling from this news," he said. "Anyone who owns a pipe organ, you never ever consider the job of having to rip it out when it's been there for so many years."
The organ was about the size of two double bedrooms and had been at the Hollywood Cinema for 32 years, he said.
The trust has owned the organ since 1993, when it was offered up for sale. As the instrument was "a tired old box of whistles" at the time, $100,000 was raised for its restoration.
"When the thing goes into a box, that $100k that we've spent on it starts to break down," Mr Duncan said. "[The organ is] voiced for the room, so a lot of money has been spent with an organ voicer so it sounds right for that particular room.
"We're really hoping we can find someone who wants to take the building on, maybe as a performing arts centre."
Mr Duncan said the trust had received great support from the Whau Local Board, the Trust Charitable Foundation, the Lion Foundation and Foundation North.
Kenneth Double, president and chief executive of the American Theatre Organ Society, expressed his support for the Hollywood Theatre Wurlitzer via email.
"News of the possible closing of the theatre, and the need to find the Wurlitzer a new home, is most distressing for those of us who love these great instruments and the music they create," he said.
The Wurlitzer's final tune at the Hollywood Cinema will be on August 30, with a performance by American organist Jelani Eddington.
Eddington will also perform a "Save the Wurlitzer" show on August 29, to showcase the instrument's versatility and raise funds for its removal and safe storage.
