She was 84.
Hamama, one of the most acclaimed and celebrated actresses and producers in the history of Egyptian and Arab cinema, performed in about 103 Egyptian movies.
Hamama was married to the star of Lawrence of Arabia and Doctor Zhivago, Egyptian actor Sharif from 1955 to 1974.
She often starred with Sharif, who was born a Christian but converted to Islam to marry Hamama and described her as the only love of his life.
They divorced in 1974 when Sharif launched a career in Hollywood.
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The actress was hospitalised earlier due to illness but had returned home, it said.
"Egypt and the Arab world have lost a creative and artistic talent who enriched Egyptian art with her sophisticated performances," the presidency said in a statement.
Hamama's career reached its peak in the 1940s and 1950s. She was chosen 'Star of the Century' by the Egyptian Writers and Critics organisation at the 2001 Alexandria International Film Festival.
Born in 1931, Hamama, made her debut in the Egyptian cinema in 1939, when she was only eight-year-old in the black and white movie 'Youm Saeed' (Happy Day).