The ink drawing, in her distinctive black and white, dates from 1928 and was created when the artist was 20.
It has been put up for auction at McTears by a private collector.
Her family only became aware of the work - 'Diaphenia like the daffadownlilly, white as the sun fair as the lily,' when they were contacted by McTears.
It will be auctioned on Thursday and is expected to sell for thousands.
Hannah Frank was born in 1908 in the Gorbals and was the last link to the Scottish Art Nouveau movement.
She died in 2008 at the age of 100 and in 2009 became the first person ever to receive a posthumous honorary doctorate from Glasgow University.
Hannah's niece Fiona Frank said she was "astounded" by the find.
She said: "I know nothing, so far, about how this beautiful drawing, done when my aunt was 20, has so far escaped our attention, or what has happened to it in the 86 years since it was first produced.It is beautiful, and although drawn when she was only 20, already displays so much of her maturity and individual, unmistakable style - and includes a reference to her love of poetry.
"I can't wait to go to the auction and see who bids."
Natasha Raskin, of McTears, said: "We can't discuss the owner but it was a private collection. The interesting thing about the drawing is that it was not known to the artist's family. It's a really, really beautiful drawing on ink and paper, which is such an unforgiving medium.
"There has been interest already from people enquiring about the condition of the drawing."