Career
After retiring as a hockey player, he became a firefighter. He was drafted by the National Hockey League"s (National Hockey League) Los Angeles Kings in the first round (twenty-first overall) of the 1998 National Hockey League Entry Draft. New York Islanders traded Žigmund Pálffy, Bryan Smolinski, Marcel Cousineau and 4th round selection (previously acquired from the New Jersey Devils - Daniel Johansson) in 1999 to the Los Angeles Kings for Olli Jokinen, Josh Green, Mathieu Biron and 1st round selection (Taylor Pyatt) in 1999.
Biron was traded to the Canadiens on December 15, 2006 via a trade with the San Jose Sharks for Patrick Traverse.
His last season in the National Hockey League came in 2005-2006, when he made 52 appearances for the Washington Capitals. He then spent two years in the AHL, playing for the Worcester Sharks and Hamilton Bulldogs.
Biron signed with the Frankfurt Lions of the German top-flight Deutsche Eishockey Liga (DEL) for the 2008-2009 season and moved to fellow DEL team Hamburg Freezers for the 2009-2010 campaign. From 2010 to 2012 he turned out for Thetford Mines Isothermic in the LNAH. After his hockey career, Biron became a firefighter in Lévis, Quebec.