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.
A banjo ukulele owned by popular 1930s and 40s entertainer George Formby is to be auctioned, with an estimated sale price of £30,000.