The Swedish star achieved global success in the 1990s with hits like Joyride, The Look and It Must Have Been Love, from the film Pretty Woman.
A statement said the singer had died on Monday, 9 December "following a 17-year long battle with cancer".
"You were the most wonderful friend for over 40 years," her bandmate Per Gessle said. "Things will never be the same."
Fredriksson was first diagnosed with a brain tumour in 2002, after collapsing in her kitchen following a workout.
The tumour cost her the vision in her right eye - but after three years of treatment, she returned to public life and toured successfully again with Roxette from 2008 to 2016.
However, the cancer eventually returned: Fredriksson's family said she had died following a recurrence of "her previous illness" earlier this week.
"Thank you, Marie, thanks for everything," said Gessle in a heartfelt statement.
"You were an outstanding musician, a master of the voice, an amazing performer. Thanks for painting my black and white songs in the most beautiful colours. You were the most wonderful friend for over 40 years.
"I'm proud, honoured and happy to have been able to share so much of your time, talent, warmth, generosity and sense of humour. All my love goes out to you and your family."
"Marie leaves us a grand musical legacy," added her manager Marie Dimberg.
"Her amazing voice - both strong and sensitive - and her magical live performances will be remembered by all of us who were lucky enough to witness them. But we also remember a wonderful person with a huge appetite for life, and woman with a very big heart who cared for everybody she met."