Ms Ginsburg, a liberal judge venerated by many on the American left, died of metastatic pancreatic cancer, the court announced on Friday.
Considered by many in the US to be a feminist icon, Ms Ginsburg was the second woman to be nominated to the highest court in the country and spent much of her career calling for gender equality.
A household name in the US, she was an unlikely cult figure among many young people, earning the nickname The Notorious RBG, inspired by the rapper Notorious BIG.
Her early life was adapted into a 2018 film titled On The Basis Of Sex, starring British actress Felicity Jones in the lead role and Armie Hammer as her late husband Martin.
Her death may give Donald Trump the chance to announce a more conservative replacement judge on the Supreme Court bench ahead of November's election, a move likely to have a significant impact on US politics.
Ms Ginsburg was a hero to many in Hollywood and following her death, celebrities were quick to pay tribute while voicing concerns over who could replace her.
Comedian Sarah Silverman said: "RIP RBG. Gutted. Sad. Grateful for all she did. And very very scared."
Oscar-winning actress Octavia Spencer wrote: "She tried to hang in there for us!! Soar on angel's wings."
In her tribute, writer and actress Mindy Kaling said: "Ruth Bader Ginsburg was the kind of scholar and patriot you get excited about explaining to your kids. The kind of person who you say 'who knows, one day you could be HER'. I hope you rest well, RBG, you must have been tired from changing the world."
Julie Cohen co-directed the 2018 documentary RBG and shared her brief tribute on Twitter.
"WHAT A LOSS," she said. Cohen later posted a picture of her and her RBG co-director Betsy West with the subject of the film, writing: "Surely the smartest and toughest person I'll ever have the privilege to know. Rest in Peace, Ruth Bader Ginsburg."
Actress January Jones shared an old picture of Ms Ginsburg and said: "Rest in sweet peace to this beautiful champion of the people. Please vote."
Ruby Rose, the Australian actress and model, posted: "I don't know what to say. My heart is broken."
British model Cara Delevingne posted a picture of Ms Ginsburg holding up her fist in a show of solidarity and said: "Trailblazer. Icon. Legend. Role model. Fighter. The true definition of an empowered woman - this is a heartbreaking loss for us all. Please, please, please VOTE in her honour."
Scandal star Kerry Washington commented: "Her rest is earned. It is our turn to fight."
Julia Louis-Dreyfus, best known for her work on satirical comedy Veep, said: "If there is a God, may She bless and keep RBG."
Marvel star Robert Downey Jr shared a picture of the late judge alongside a quote said to have been made by her.
Downey Jr said: "'Fight for the things you care about, but do it in a way that will lead others to join you.' RIP, RBG."
Mariah Carey also paid tribute, writing on Instagram: "Thank you for a lifetime of service. Thank you for changing history. We will never let it be undone. RIP RBG."
TV presenter Jameela Jamil commented: "What an icon we have lost."
And Queer Eye star Jonathan Van Ness said: "Thank you for everything you stood for. Vote everyone, Vote."
US TV personality and former Strictly Come Dancing star Michelle Visage said Ms Ginsburg's death left a "massive hole in democracy".
She wrote: "You, my lady, were a beacon of strength, light, hope and love!!!! You are appreciated more than you will ever know."
The Supreme Court is crucial in the US as its nine members can hold the final say on key issues such as abortion, gun control and healthcare.