Murphy was selected by the Carolina Hurricanes in the sixth round of the 2008 NHL Entry Draft with the 165th overall pick. On March 18, 2009, he signed a three-year, entry-level contract with the Hurricanes. In 2007–08, Murphy led the Belleville Bulls to the finals of the J. Ross Robertson Cup, the OHL championship series, but they lost Game 7 to the Kitchener Rangers.
He became the first back-to-back winner of the OHL Goaltender of the Year award on April 27, 2009, after being awarded the honor for the second straight year.
On December 6, 2011, Murphy was temporarily promoted to the Carolina Hurricanes from their AHL affiliate, the Charlotte Checkers. That same night, Murphy became the first goalie in NHL history to record a loss before allowing his first NHL Goal against.
On June 6, 2012, Murphy left the Hurricanes and signed a one-year deal in the Russian Kontinental Hockey League with Spartak Moscow. During the 2012–13
season, Murphy started in only 7 games with Spartak before opting for a
release to return to the Charlotte Checkers on March 26, 2013.
On July 11, 2013, Murphy was officially returned to the Carolina Hurricanes system, signing to a one-year, two-way contract.
On June 16, 2014, Murphy opted to return to Europe in siging a one-year contract with Austrian club, Dornbirner EC of the EBEL.