Hansons Auctioneers said the Gibson UB3 banjolele is expected to attract worldwide interest at the sale on 30 June, in Etwall, Derbyshire.
In 2008, another George Formby banjo ukulele sold for for £72,000 at auction to Queen's Brian May.
In 1936, the BBC banned Formby's song The Window Cleaner for being smutty.
John Croft, former president of the George Formby Society and ukulele expert, said: "There is huge interest in this instrument. George Formby has fans all over the world - young and old."
Mr Croft, from Llanyblodwel, Shropshire, added it was a "wonderful piece of social history".
"In his heyday in the late 1930s, George Formby earned more than three top Hollywood stars put together - Errol Flynn, Douglas Fairbanks and Clark Gable.
"And we should never forget Formby's contribution to boosting morale among the troops during World War Two.
"He and his wife Beryl flew out to dangerous war zones, including El Alamein. This country owes a great deal to them both.
"I hope the instrument stays in the UK but the most important thing is that it is loved and played."
This banjolele was originally purchased by Bill Logan, the first president of the George Formby Society.
Who was George Formby?
He was born George Hoy Booth on 26 May 1904, in Wigan and was the eldest of seven children
The actor, singer-songwriter and comedian's show business career started in 1921 and lasted 40 years until his death in 1961
He was famous for playing the banjolele and by 1939 was the most popular and highest paid entertainer in the British Isles - he was estimated to be earning more than £100,000 a year
Formby appeared in 21 films, made more than 230 records, entertained on stage hundreds of times, performed twice by royal command and entertained an estimated three million allied servicemen and women during World War Two
In 1960, Formby made his last record, Happy Go Lucky Me, and in December that year made what was his final television programme, The Friday Show
George Formby Society
Charles Hanson, owner of Hansons Auctioneers, said: "This is such a rare opportunity. This was one of George Formby's favourite banjoleles and the chance to own and play it is very special. This instrument is a priceless treasure for Formby fans."
Formby was said to have owned three Gibson UB3 models.

Robinson was left upset by a number of refereeing decisions as his side conceded twice in the final three minutes to draw 3-3 at home to Bristol Rovers in League One on Tuesday.
"Maybe we need to cheat a little bit more, go down, scream, maybe we need to do that," he told BBC Three Counties.
"Honesty in the way we're doing things doesn't seem to be getting the right rewards."
After relegation from the Championship, MK Dons have won just four times in League One this season and have not recorded a home victory in 12 league games - a record that stretches back to March.
"Stay on your feet, be disciplined, but you've seen tonight that's clearly not the case," added Robinson, who has been in charge of the club since May 2010.
"If you stay on your feet you don't get the foul. Ultimately you lose the football and you get countered on or you get kicked in your own area by a centre forward who finds himself two yards out tapping it in."

Mr Hunter, 64, was knocked down and killed on a road in the Arab state at the weekend.
The father-of-two was working as a media consultant for Northern Ireland Co-operation Overseas (NI-CO).
The organisation sends local experts to advise state bodies abroad.
A banjo ukulele owned by popular 1930s and 40s entertainer George Formby is to be auctioned, with an estimated sale price of £30,000.
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Manager Karl Robinson says MK Dons may have to "cheat more" to win matches.
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A man has been arrested by police in Bahrain in connection with the death of former BBC journalist and News Letter editor Austin Hunter.