Portrait of Baranowski was painted in Paris in 1918 and is considered one of the artist's most distinguished works. Sir Robert acquired it in 1937.
Sir Robert and his wife are already major benefactors of the university, having loaned their entire art collection in 1973.
The Sainsbury Centre for Visual Arts was opened to the public some five years later and also houses the school of world art and museology. The Modigliani was part of the original collection and has been on display at the centre since its opening.
Sir Robert has now decided to sell it to raise money for the Japanese unit.
Anne Ogden, spokeswoman for the university, said the Sainsbury Centre was due to celebrate its 20th anniversary next week.
"The original collection comprises thousands of paintings and sculptures. There are paintings by Henry Moore and Francis Bacon and artefacts from all over the world."
She said the university was chosen because Sir Robert's daughter, Annabel Kanubus, studied maths and physics there in the late 1960s. "Sir Robert had already decided that he would like to give their collection to a university and have it displayed in a public building. He offered it to us and as we were a very new university at the time we were delighted to accept."
The original collection contains several Japanese pieces and Ms Ogden said that Sir Robert was keen to set up a research centre for Japanese cultural studies. "He is very interested in Japan and has been buying works from there for a number of years," she said.
Dame Elizabeth Esteve-Coll, adviser to the Sainsbury Collection and former vice-chancellor of the university, said the centre would provide a tremendous boost to the study of Japanese culture in Britain. Melanie Chore, deputy chairman of Sotheby's Europe and head of the company's Impressionist and Modern Art Department in London, said: "It is a great privilege to be asked to sell such a beautiful portrait. It is double rewarding to know that the proceeds are going to set up such a worthwhile educational enterprise."
In his brief working life at the forefront of Parisian avant-garde, Modigliani established himself as one of the most important artists of the 20th century.
Portrait of Baranowksi was painted two years before his death in 1920, aged 36. Baranowski was a young Polish emigre and, although he never wrote any verse, the painting has become known as The Poet.Reuse content