The musician was best known for being the bass player for the legendary Booker T & the MGs, but also appeared on such classics as Otis Redding's 'Respect' and Sam and Dave's 'Hold On I'm Comin''.
Dunn is said to have died in his sleep while on tour in Japan for a series of concerts.
His friend and tourmate Steve Cropper confirmed the news on his Facebook page, writing: "Today I lost my best friend.
"The World has lost the best guy and bass player to ever live."
Dunn's bass skills were heard on a host of hit records for the Stax record label, including 'Soul Man' and 'Try a Little Tenderness'.
He also featured on many Booker T & the MGs classics, such as 'Green Onions' and 'Time is Tight'.
Later in his career he worked with the likes of Eric Clapton, Neil Young, Stevie Nicks and Rod Stewart, while he played himself in the 1980 movie The Blues Brothers and its 2000 sequel.
Booker T & the MGs were inducted into the Rock and Roll Hall of Fame in 1992 and Dunn himself received a lifetime achievement Grammy award in 2007.
Watch Booker T & the MGs perform 'Green Onions' below: