An anonymous donor from America has given a university in Australia a Picasso painting worth up to £12 million on the condition that it be sold and the money raised be spent on research into obesity.

Pablo Picasso's 1935 painting Jeune fille endormie

The donor flew to Australia from the US last year to personally hand over the painting, "Jeune fille endormie", which is one of the largest gifts ever made to the University of Sydney.

The vivid painting, which measures 18 inches tall by 22 inches wide, was painted in 1935 and depicts Picasso's lover and muse, Marie-Therese Walter. It has only been shown once in public before now.

In June, the artwork, which shows Walter asleep with her head leaning on her crossed arms, will be sold at Christie's auction house in London and is expected to fetch between £9 million and £12 million. Last year, a 1932 portrait of Walter by Picasso, "Nu au Plateau de Sculpteur" set a world record when it was snapped up by a mystery bidder for $106.5 million (£65m).

Michael Spence, Sydney University vice-chancellor, said the "extraordinary act of generosity" came with three conditions.

"First, that the donor remain anonymous, second that the painting be sold and the proceeds be used for scientific research, and third, that the gift be recognised in particular ways which we will be announcing in due course," he told the Australian Broadcasting Corporation.

Dr Spence said money raised by the sale would go towards funding a new centre for obesity, diabetes and cardiovascular disease.

Giovanna Bertazzoni, director of impressionist and modern art at the auction house, said she expected keen interest from collectors in Asia, the Middle East and Russia, as well as Europe and the United States.

"This is an absolute jewel of a painting by one of the great artistic geniuses of Western art."

Picasso met Walter when he was 45 and she was 17 outside the Galeries Lafayette in Paris in 1927, while he was still married to Olga Khoklova.