In a statement, the star said she was cancelling her planned summer tour of Scandinavia after discovering a lump on her breast. She said she would be operated on soon, and would then face follow-up treatment.
"To be hit by this turns your whole life upside down, not least when you have a family with three children, as I do," she said.
She asked the press not to request any interviews with her about the illness.
"I'm going to take it one day at a time, and devote the near future to getting through whatever is needed, together with my family, and hopefully getting better soon."
Grönvall is a regular in Melodifestivalen, the national competition that decides Sweden's entry to the Eurovision Song Contest. She recently completed a run in the musical Sweet Charity in Stockholm, for which she won critical acclaim.
She had planned to sing together with fellow stars Charlotte Perrelli and Christer Sjögren in The Heart Break Tour this summer.