The album reportedly sold only 5,000 copies in the UK, and the band was dropped by Uni not long afterward.
In 2011 Michael Gira stated, "I abhor that record. Bill Laswell is a very good producer, but we didn't mesh well. I was intimidated and sang in this cramped, monotone way. It didn't sell, and we got dropped." The album was reissued on CD by Water Records in 2012.
AllMusic wrote, "Ultimately, Burning sounds more like a compromised major label Laswell project than a Swans album, to its overall detriment", calling the album a "general disappointment". On the other hand, Trouser Press was favorable, writing "The Burning World benefits a great deal from the world music instrumentation and structural abilities Laswell brings to it. The arrangements are uniformly strong, the gentler sounds don't strike one as a compromise and the cover of Blind Faith's "Can't Find My Way Home" is both apt and surprising", ultimately calling the album "a nice one that's almost as haunting as it wants to be."