"In one of the darkest moments of our lives, we are not able to find the appropriate words to express the pain in our heart", part of her statement to the AP read, per NBC News.
They have said funeral arrangements will be announced "in the coming days".
On the announcement of her death, tributes immediately began pouring in as music lovers remembered her sterling career.
A fierce musical talent not only in sensitive and dynamic vocal interpretation but also as a skilled pianist and arranger, Franklin demanded respect from us. "Everything she's thinking or dealing with is all in the music, from "Chain of Fools" to "Respect" to her live performances".
Franklin's voice - a powerful instrument that could instantly go from smooth and smothering to powerful and piercing - was unmistakable. "She is the reason why women want to sing".
She performed at the inaugurations of two United States presidents, delivering a stirring rendition of "My Country 'Tis of Thee" at the January 2009 ceremony for Barack Obama, the first African-American president, while wearing a widely remarked grey hat with a big bow.
Franklin's ability to survive personal and professional storms added to her legacy and ensured that her title as royalty in R&B music would not pass on to anyone else.
Her dad, C.L. Franklin was one of the most well-known Baptist ministers of his generation.
In 1970, after their marriage broke down, Jet magazine reported that White was investigated for shooting Sam Cooke's brother, who attempted to protect Franklin when her husband turned up at her house. From there, Franklin's music career, which spanned gospel, R&B, soul, and pop, took off. In 1987, she became the first woman to be inducted into the Rock & Roll Hall of Fame and won 18 Grammy awards across half a century.
The legendary singer was born in Memphis, Tennessee, on March 25, 1942.More news: Whalen to retire from WNBA at season's end; ready to coach Gophers
Before she was five, the family moved to Detroit where her father had been given the pastorship of a church.
American soul singer Aretha Franklin is seen on May 16, 1968, when she was a young star on the Atlantic record label.
'The greatest singer of all time.
That same year, Detroit named a street after her.
With Obama, in particular, Franklin shared a special bond. 'Not only was she a uniquely brilliant singer but her commitment to civil rights made an indelible impact on the world, ' she continued.
"She's very ill. She has been under the weather for months". "She is truly an immortal artist who we'll love and respect forever". "Just like her mom, she was one of the great sopranos".
"It's hard to even think that I'm referring to her in the past tense right now", he said, his voice cracking. The 76-year-old announced plans to retire last year, saying she would perform at "some select things".
Amid decades of stardom, Franklin was conspicuously tight-lipped about her personal life.
She is survived by four sons: Clarence, Edward, Ted and Kecalf. She was surrounded by family and friends at the time of her passing. Aretha would marry a second time, to Glynn Turman, in 1978.
Her 1967 song Respect demanded common decency be shown to women, and paved the way for celebrity feminism - some 50 years before it manifested with the #MeToo and #TimesUp movements of today.