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.
