Hamama, who made her screen debut at seven years old, died on Saturday aged 83, after a career spanning seven decades and almost 100 films alongside masters of Egypt's film industry, including Youssef Chahine.
"Egypt says goodbye to the lady of the screen," said a banner carried by fans, as Hamama's body was taken from a mosque in Cairo's October 6 neighbourhood for burial at her family cemetery, an AFP photographer said.
Some fans took selfies on their mobile phones with film stars and politicians who attended the funeral.
"Faten Hamama was an exceptional ambassador for Egypt... she spread love and beauty wherever she went," said former Arab League chief Amr Moussa, who attended the funeral.
Prime Minister Ibrahim Mahlab said Egypt's arts scene had "lost one of its principal pillars".
"Faten Hamama will remain as one of the icons of Egyptian and Arabic fine arts that has contributed to forming and elevating Arabic awareness," Arab League chief Nabil al-Arabi said in a statement.
Hamama often starred in films with Omar Sharif. Born a Christian, he converted to Islam to marry Hamama and described her as the only love of his life.
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The couple appeared together in the 1961 movie "River of Love", based on Leo Tolstoy's "Anna Karenina".
They divorced in 1974 when Sharif, already famous in his homeland, launched a career in Hollywood.
"The lady of the Arabic screen," as she was known, suffered "a sudden health problem which led to her death," Egypt's official news agency MENA reported Saturday.
MENA said she had been hospitalised weeks earlier due to illness but had returned home.
"Egypt and the Arab world have lost a creative and artistic talent who enriched Egyptian art with her sophisticated performances," a statement from the president's office said.
A leading light in the golden age of Egyptian cinema, Hamama's career reached its pinnacle in the 1940s and 1950s.
She starred in romantic movies alongside the famed Arab crooner Abdel Halim Hafez as well as in films advocating women's rights and condemning social injustices.
Hamama had a daughter, Nadia, from a previous marriage and tied the knot for a third time with doctor Mohamed Abdel Wahab.