The Sugarcubes took off after they became the focus of the music press after forming in 1986 but they only had one top 20 single, in Britain, with "Hit" in 1992, the BBC reported Wednesday.
The band members went their separate ways soon after that, with Bjork leaving to pursue a solo career. Her solo album brought her five hit singles and two Brit awards.
All profits from the concert will go to the band's record label, Bad Taste. A statement on Bjork's Web site said the profits would allow the company to "continue to work on a non-profit basis for the future betterment of Icelandic music."