Muir went undrafted through his junior career with the University of New Hampshire and signed his first pro contract with the Edmonton Oilers. Muir is considered a journeyman defenceman having also played stints for the New Jersey Devils, Chicago Blackhawks, Tampa Bay Lightning, Colorado Avalanche, Los Angeles Kings and the Washington Capitals.
His most distinguished year came in the 2005–06 season for the Capitals where he played 72 games for 8 goals, 18 assists and 26 points.[1]
On August 5, 2008, Muir signed with Belarusian club HC Dinamo Minsk to participate in the newly formed KHL. Minsk released him after 23 games in the KHL, and in early January 2008 he signed with German club Frankfurt Lions for the remainder of the DEL season; after the Lions' quick exit from the 2009 DEL playoffs the club declined to offer Muir a contract extension.[2]
Muir joined senior MLH team the Brantford Blast in 2011.[citation needed]