Cobain played the retro acoustic-electric 1959 Martin D-18E during a legendary MTV Unplugged performance in 1993, just five months before he died.
At $6.01m after fees, the guitar is the most expensive ever sold at auction, Julien's Auctions said.
Bidding in Los Angeles opened at $1m and was won by Rode Microphones founder Peter Freedman.
Nirvana's acoustic performance for the MTV Unplugged series on 18 November 1993 is now considered one of history's greatest live performances.
