That would be a record price of any musical instrument—sold privately or at auction, according to Sotheby's.
This viola was crafted by Antonio Stradivari in 1719. It as known as "The Macdonald," named for the 3rd Baron Macdonald, Godfrey Bosville, who acquired it in the 1820s.
It's one of only two Stradivarius violas still in private hands.
About 600 instruments made by the Cremonese master survive, but only 10 are violas, said Tim Ingles, director of the London-based fine instruments auction house Ingles & Hayday, which is conducting the sale with Sotheby's.
"The finest is of all the violas is generally agreed to be 'The Macdonald' of 1719," he said in a video on Sotheby's website.
Check out the video here.
It's being sold by the estate of Peter Schidlof, co-founder of the Amadeus Quartet who acquired it in 1964 and died in 1987.
Potential buyers can submit sealed bids. The highest bidder will be announced June 25.
The auction record for a musical instrument is the 1721 "Lady Blunt" Stradivarius violin, which sold online for $15.9 million in 2011. It was sold by the Nippon Music Foundation, which used the proceeds to aid victims of Japan's 2011 earthquake and tsunami.
—By CNBC's Marty Steinberg. The Associated Press contributed to this story.