The surprise news was delivered in the form of a statement on the eccentric star's official website.
"Nearly 20 years ago The Sugarcubes put out on their own label Smekkleysa SM, their first single Birthday," it said. "This release was the start to the splendid career of The Sugarcubes, and impressive releases of Icelandic artists in Iceland and abroad alike."
The one-off gig is designed to raise funds "for the future betterment of Icelandic music and artists," by helping to fund their record label.
In spite of wide critical acclaim in Britain, The Sugarcubes only managed one Top 40 single, with 'Hit' reaching number 17 in January 1992. Bjork left the band later that year and launched a popular, and sometimes controversial, solo career in 1993.