"Like people all around the world, Hillary and I are thinking about Aretha Franklin tonight and listening to her music that has been such an important part of our lives the last 50 years", wrote Clinton.
US President Donald Trump also paid tribute to Franklin as "a great woman, with a wonderful gift from God, her voice".
"She will be missed but the memory of her greatness as a musician and a fine human being will live with us forever", he tweeted.
Gwendolyn Quinn said the singer died at her home in Detroit on Thursday morning where she was surrounded by friends and family. The singer has penned numerous charting singles such as "Respect", "I Never Loved a Man", "Chain of Fools", "Baby I Love You", and "I Say a Little Prayer".
The statement concluded: "As we grieve, we ask that you respect our privacy during this hard time".
Funeral arrangements will be announced in the coming days, the statement said, according to CNN.
Aretha Franklin may be best remembered for her voice and chart-topping hits, but her renditions of the national anthem before a number of sporting events will go down as some of the best ever. "Michelle and I send our prayers and warmest sympathies to her family and all those moved by her song".
She subsequently got engaged to longtime friend Willie Wilkerson, but things were called off in 2012. But Aretha did and she raised the roof.
Born March 25, 1942, in Memphis, Tennessee, to C.L. Franklin, the most prominent black Baptist preacher in America during the mid-20th century, and a gospel singer, Aretha Louise Franklin began performing in front of her father's congregation at New Bethel Baptist Church in Detroit, which she considered her hometown.
In February of 2017, Franklin announced that she would stop touring, but she continued to book concerts. "She was really important to our community and it's a great loss". In 2009, for the inauguration of Barack Obama, she performed "My Country, 'Tis of Thee".
In 2014, she released an album of covers from across the soul spectrum - not just Prince's "Nothing Compares 2 U", but also Adele's "Rolling in the Deep".
In a statement to Us Weekly, she said: "I'm doing well generally, all tests have come back good".
Franklin is survived by her four sons - Ted White Jr., Kecalf Cunningham, Clarence Franklin, and Edward Franklin - and several grandchildren.