The original 1940s Gretsch Synchromatic 160 guitar from the 1987 video will be the highlight of the auction Faith & Fame: A Personal George Michael Collection on October 29.
The video features Michael wearing a black leather jacket and blue jeans, playing the guitar next to a jukebox.
The song, from Michael's debut solo album of the same name, spent four weeks at number one on the US Billboard Hot 100 and reached number two in the UK.
The collection featuring the guitar was assembled by Michael's former personal assistant, Siobhan Bailey, amassed during her 20 years working with him.
Bailey died in 2014 and her personal archive is being offered for auction by her widower.
Other items include ring-bound tour itineraries from Michael's solo career and his time in the band Wham!
There is also memorabilia from some of his most celebrated live performances, including a four-page running order from Live Aid in 1985 which features his duet with Elton John, Don't Let The Sun Go Down On Me.
For fans of his recordings, there are numerous presentation discs and gold records celebrating milestone sales, including a gold disc for 500,000 UK sales of Wake Me Up Before You Go-Go.
The archive as a whole is expected to achieve more than £200,000 ($A376,000).
Guy Schooling, chairman of Sworders auctioneers, said: "George Michael's work continues to resonate as powerfully today as it did during his heyday.
"The Faith guitar is the jewel in the crown, together with the other items from Siobhan Bailey's collection, it tells a story of creativity, ambition and artistry on a global scale.
"The sale will offer avid fans around the globe the chance to own not just pieces of music history, but objects that capture the spirit and ambition of one of pop's greatest and most-loved artists."
Michael, born Georgios Kyriacos Panayiotou, had 13 number one singles in the UK.
He came out as gay in 1998 and became an activist for LGBTQI rights and an HIV/Aids charity fundraiser.
Michael died of heart disease on Christmas Day 2016 aged 53.
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