Four other people were injured, one seriously, in the blast at the Centraco site, owned by French power utility EDF and adjacent to the Marcoule nuclear research centre. The site does not house any nuclear reactors.
The furnace that exploded is used to melt waste with levels of radioactivity ranging from low to very high, ASN said.
It did not immediately give a reason for the blast but said it was completely contained within the furnace.
Police also said there was no contamination outside the site, which is about 30 km (18 miles) from the city of Avignon and about 80 km (50 miles) from the Mediterranean coast.
France -- the world's most nuclear-reliant country -- is carrying out stress tests on its 58 nuclear reactors in the aftermath of the Fukushima disaster in Japan.