The olive green mohair cardigan epitomised the fashion of the grunge-scene of the early 1990s, and even has a burn hole in one of the pockets.
It is estimated to sell for up to £245,000.
The MTV gig, which took place in November 1993, featured many of the band’s lesser-known hits and covers.
It is widely considered to be one of Nirvana’s most defining performances.
A turquoise custom-built Fender guitar which Cobain played during the band’s In Utero tour will also go under the hammer.
The left-handed guitar, which was made in 1993, was previously on display at the Rock and Roll Hall of Fame.
Cobain’s wife, Courtney Love has written an accompanying letter of provenance, saying it was one of his favourite guitars.
The instrument could raise up to £409,000.
Cobain died on 5 April 1994, aged just 27, from a self-inflicted gunshot wound to the head.
Earlier this year, Cobain’s daughter Frances Bean curated a new clothing line to celebrate the legacy of her father.
Other pieces in the two-day auction of rock memorabilia include handwritten lyrics by Bob Dylan, Eric Clapton and Bruce Springsteen.
It will take place later this month.