Muršak developed his skills in his hometown ice hockey club HDK Maribor where he played until the age of 17. As a youth, he played in the 2001 and 2002 Quebec International Pee-Wee Hockey Tournaments with a team from Slovenia. He later transferred to Czech club HC Ceské Budejovice for which he played for a season in CZE-U20 youth development league. In 2006 he was selected by the Detroit Red Wings as the 182nd overall draft pick. During the same year Muršak was drafted by the Saginaw Spirit in 1st Round of the 2006 CHL Import Draft, 33rd overall. He had a successful first season for Saginaw which earned him a playoff call up for the Grand Rapids Griffins, AHL affiliate to the Detroit Red Wings. In his second OHL season, Muršak was traded from the Saginaw Spirit, to the Belleville Bulls where he stayed until the end of the season, before moving on to play regularly for Grand Rapids in the AHL.
Detroit Red Wings
Muršak signed a contract with the Detroit Red Wings in April 2007. Since his draft in 2006 he has made appearances for the Red Wings during training camps. On 26 December 2010 it was announced by Detroit that Muršak was called up to the team to fill in after an ankle injury of Danny Cleary. He made his NHL career debut on 28 December 2010 in a game against the Colorado Avalanche, thus becoming the second Slovenian, after Anže Kopitar of the Los Angeles Kings, to play in the NHL. Muršak scored his first NHL goal on 10 January 2011, also in a game against the Avalanche against Peter Budaj. On 17 February 2011, Muršak signed a new two-year contract with the Red Wings. Due to the 2012 NHL lockout, Muršak signed a temporary contract with the Slovenian hockey team HDD Olimpija Ljubljana of the EBEL league. In 30 games with Olimpija, he excelled with 48 points, before returning for the start of the shortened 2012–13 season with the Red Wings. On opening night, he was again setback by injury, after hurting his collarbone in a 6–0 defeat against the St. Louis Blues. On his return to health, and with limited opportunity with the Red Wings, Muršak was placed on waivers on 22 February 2013. He was assigned to the Griffins for the remainder of the season.
Return to Europe
As an impending free agent, Mursak subsequently moved to Amur Khabarovsk of the Kontinental Hockey League. After re-establishing his offensive presence in three and half seasons with CSKA Moscow, Muršak left the club as a free agent and opted to continue in the KHL in signing a one-year contract with Torpedo Nizhny Novogord on May 1, 2017. Mursak then played for Frolunda HC in the SHL and scored a brace on his first team game debut against HV71 on January 11, 2018. Mursak currently plays for SC Bern in the NL.