The novelist, who won the Booker for her novel "Hotel du Lac", died peacefully in her sleep on Thursday, according to a notice of her death in The Times newspaper.
The only child of secular Polish Jews who settled in London, Brookner was born in 1928.
She studied art history before becoming the first woman to hold the Slade Professorship of Fine Art -- the oldest professorship of art at the universities of Cambridge, Oxford and London.
"Hotel du Lac", centred on a romance novelist staying on the shores of Lake Geneva, was a surprise winner.
Her novels often involved lonely female protagonists.
She was made a Commander of the Order of the British Empire, one step below a knighthood, in 1990.
Her last book was "At The Hairdresser's", a novella published in 2011.
Brookner was a "wonderful writer who had this wonderful lucid prose... She was an icon of my age", British novelist Jilly Cooper told The Times.
Orange Prize-winning novelist Linda Grant called her an "underrated master of incisive fiction and laser prose".
Brookner never married and had no children. At her request there will be no funeral, the notice in The Times said.
