Mun was born in Seoul. He is the youngest of the three siblings with two older sisters. He attended Daechi Elementary School located in Seoul. When his family moved to the U.S, he went to John Burroughs Middle School located in Los Angeles. Mun spent his years of high school at Parks Junior High School and Sunny Hills High School, both of which are located in Fullerton, California. In 1996 he returned to Korea and he joined SM Entertainment as a trainee and was featured as a Rapper on label mate girl group S.E.S.' single "I'm Your Girl" along with Andy. On March 24, 1998, with the stage name Eric, he debuted as leader and main Rapper of group Shinhwa with their single "해결사" (The Solver) on KM Music Tank. He stated that their debut album, Resolver, did not perform well and the band almost disbanded. At the time, he thought seriously about giving up and returning to the U.S.
In 2002, Mun and his Shinhwa bandmates had cameo appearance in the movie Emergency 19 Act. In 2003 Director Park Sung-soo cast him in a supporting role for MBC’s series Breathless (I Run). In early 2004, he appeared in the drama [Phoenix (2004 TV series)|Phoenix]] (Bulsae).
In 2005, Mun starred in lead role in MBC's Super Rookie with Actress Han Ga-in. It was also broadcast on Fuji Television. It got solid rating in Korea during the broadcast. Super Rookie was also a big hit in Japan after Fuji TV paid ₩2 billion for the broadcast rights in Japan. It was commercially successful in Japan when it was broadcast there. In December 2005, Mun went to promote Super Rookie in Japan, where he was greeted at the airport by a large crowd.
In early 2006, Mun was injured on the set of MBC drama Wolf, resulting in it being pulled off air after four episodes. Mun was injured whilst shooting a scene, near Namdaemun in Seoul, where he was to save co-star Han Ji-min from being run over by a car. However the stunt car driver misunderstood the signals drove at them at 40 km/h and did not stop in front of them as planned.
Shinhwa's 10th Anniversary concert in March 2008, that marked the start of Shinhwa's hiatus as a group to fulfill mandatory military Service. Before his army enlistment, Mun appeared in a period drama for the first time in his acting career with Strongest Chil Woo. With 30 million wons per episode for Strongest Chil Woo, Mun was the highest paid singer-turned-actor in the industry at the time.
Mun gave up his American citizenship in 2003, to be able to serve his military Service. He was the first Shinhwa member to enlist for mandatory military Service in October 2008. Because of his back injury from the filming of Wolf, Mun served non-active duty pafter undergoing four weeks of basic training. He was discharged on 30 October 2010.
As part of Top Class Entertainment he produced girl group Stellar, who debuted in August 2011 with the song "Rocket Girl".
Mun's rap is featured on Brown Eyed Girls' Ga-in's digital single "Nostalgia", released on 30 November 2012.
December 2013, Mun's contract with Top Class Entertainment came to an end. He did not re-sign another contract with Top Class Entertainment and no longer has any running of group Stellar whom he helped the management to produce and promote the original line up.
Despite its average 7% Nielsen rating, Mun and the team of Discovery of Romance received praise for their acting and Mun won a 'Triple Crown at KBS 2014 Year End Award (Excellent Actor, Best Couple, and Netizen Award). With this win, Mun had won acting awards at all three major Broadcasting Networks. In 2015, Discovery of Love was nominated for the 2015 Rockie Award in the Melodrama category alongside 30 Vies (Canada), EastEnders (UK), Grey’s Anatomy (USA), My Sunshine (China), and Mysterious Summer (Japan). In an 2015 Instiz discussion post about viewers' favorite drama characters, Mun's Kang Tae-ha Discovery of Romance stays in top 10 at #6.
Mun released Shinhwa's 12th studio album We in 2015. Shinhwa broke their previous record with 10 wins (a Triple Crown at Mnet's M! Countdown) for this album. Mun and Shinhwa were on concert tour starting in May 2015, and ended with an Encore concert in Seoul in August. Shinhwa also performed at KCON LA for the first time in early August of that year.
At the end of November 2016, Mun and Shinhwa released a mini album Unchanging: Orange as part 1 of their 13th album.
After dating speculation came out from several news sources on February 23, 2017, management from both sides confirmed that Mun was dating Actress and model Na Hye-mi. It is said that they have been dating for more than four years, since the dating rumour first appeared back in 2014. On April 17, 2017, through Shinhwa Company's Facebook, Mun announced that he and Hyemi are to get married on July 1, 2017, with a private wedding ceremony at a church with family and friends.
After Shinhwa's 18 Anniversary in March, Mun returned to acting and appeared in the South Korean TV cable (tvN) drama Another Oh Hae-young with Seo Hyun-jin. The drama premiered on May 2 with better rating than its predecessor Pied Piper. It broke its projected rating of 5% of on its 6th episode and becomes tvN's all-time highest rated drama for their Monday - Tuesday time-slot with the rating of 9.9% for its final episode. Another Oh Hae-young team was rewarded a trip to Thailand after the drama ended. At tvN10 Awards on October 9, Mun was awarded the title of "Ro-co King". Seo Hyun-jin was also crowned "Ro-co Queen" for their roles in Another Oh Hae-Young.