The Fleetwood Mac singer said the liberal judge, who was venerated by many on the American left, was her “hero” who “fought for me and all women”.
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.
She died of metastatic pancreatic cancer, the Supreme Court announced on Friday.
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.
Writing on Instagram, Nicks said her death left her feeling “very much like I felt on the night my own mother died”.
“I feel like someone punched me in the stomach,” she added.
“My tears have not stopped since a friend tip-toed into my room and said, ‘Stevie, Ruth died’.”
The singer said she had hoped to meet Ms Ginsburg “to hold her hand and give her a huge hug and thank her for all she had done for women and for all she would continue to do”.
“It is my great regret that I did not make the effort to go and try to meet her,” Nicks said.
“As with all legends, you think they will live forever, so you will get there in time.”
She added: “As a two-time Rock And Roll Hall Of Fame inductee, the first female to be inducted twice, compared to 22 men having been inducted twice, I Stevie Nicks, induct Ruth Bader Ginsburg into the Rock And Roll Hall Of Fame of Life.”
A number of other celebrities have also paid tribute to Ms Ginsberg.
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.”
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.”
