It was bought by Jim Irsay, owner of the American Football team Indianapolis Colts, according to AP news agency.
Prince died from an accidental overdose at his Minnesota home in April.
The Yellow Cloud guitar was built in the late 1980s by Knut-Koupee Enterprises of Minneapolis and used in numerous concerts until the mid-1990s.
Mr Irsay is a well known collector of musical instruments. He also has items once owned by stars including Bob Dylan, Jon Lennon and Jerry Garcia of the Grateful Dead.
Last December he was reported to have bought a drum kit played by Beatles drummer Ringo Starr for $2.1m.
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