The musician had been struggling from cancer and the news is yet to be confirmed, reported Variety.
The reports started doing the rounds on social media after Hart's photograph was posted on the official Husker Du Facebook page.
The musician formed the group with bandmates Bob Mould and Greg Norton in 1979, which ushered in a new wave of punk with hardcore leanings.
Their style was, however, melodic and palatable, especially cherished by the college-going crowd of the '80s.
They released six albums from 1983-87 with 'Everything Falls Apart' and 'Warehouse: Songs and Stories'. Their 1984 set 'Zen Arcade' is considered a classic.