Thieves broke into Bjork's luxury flat in Maida Vale, west London, on Friday night and are thought to have stolen valuable recording equipment.
The 36-year-old singer and actress is believed to have been asleep in the flat at the time.
A spokeswoman for the singer refused to comment on the burglary, saying: "It's a private matter."
Other celebrities whose London homes have been burgled recently include models Jerry Hall and Elle Macpherson, Tara Palmer-Tomkinson and singer Geri Halliwell.
Actress Joan Collins, 69, has denied reports a decision to base herself in New York was because of her fear of crime in London.
Police plea
Insisting she was moving for work reasons, she did tell the Mail on Sunday: "Groups of muggers are frequently attacking people in the area where I live in London.
"And the police don't appear to be able to do anything about it."
And Liz Hurley, who was mugged at knifepoint in London eight years ago, has pleaded publicly for more police on the capital's streets, saying the US was less dangerous.
Helping to launching a drive by magazine Woman's Own for women to feel safer, Hurley said: "We definitely need a stronger police presence on the streets.
"It's rare to see them at all now. In America, uniformed cops eat in coffee shops, diners and restaurants, and I always feel safer having them around."
Brought up in a commune in Iceland, Bjork first rose to prominence with indie group The Sugarcubes.
Wider fame followed with her 1993 solo album Debut, and she has won acclaim as an actor, notably on Lars von Trier's Dancer in the Dark.