Summer had a string of hits during the disco heyday of the Seventies and remains best known for her hit I Feel Love.
She was singing from the age of 8 in her church choir and would go on to win five Grammy Awards and have huge chart success on both sides of the Atlantic.
Summer was reportedly battling cancer.
Her family said in a statement: "Early this morning we lost Donna Summer Sudano, a woman of many gifts, the greatest being her faith.
"While we grieve her passing, we are at peace celebrating her extraordinary life and her continued legacy.
"Words truly can't express how much we appreciate your prayers and love for our family at this sensitive time."
Although she fell into severe depression after the 9/11 attacks on the US, Summer recovered with the help of her faith.
She said in 2008: "I went to church and light came back into my soul. That heaviness was gone."