|Date of birth||6 May 1965|
|Place of birth||Sisak, SFR Yugoslavia|
|Height||1.80 m (5 ft 11 in)|
|* Senior club appearances and goals counted for the domestic league only.
He started his career at hometown in Mladost Petrinja in 1983 and moved to Dinamo Vinkovci in 1988. He left the club in 1993, when it was already renamed to Cibalia, and moved to Varteks Varaždin. In 1996, he left Varteks for Turkish club Beşiktaş Istanbul and spent two seasons there before eventually returning to Varaždin in 1998. By the end of his playing career, he also had a short spell with Belgian club Charleroi, but made only seven league appearances for the club and returned to Varteks, where he finished his playing career in 2000 and continued to work for the club as the first assistant coach as well as the goalkeeping coach.
Between 1995 and 1999, Mrmić won a total of 14 international caps for Croatia, mainly being the national team's second-choice goalkeeper during the period.
He made his international debut on 11 June 1995 in a 1–0 defeat to Ukraine in Kiev during the UEFA Euro 1996 qualifying, coming on as a substitute for Dubravko Pavličić in the 27th minute, following a red card to Tonči Gabrić. He made his second appearance in the qualifying on 3 September 1995 in a 7–1 win at home to Estonia, coming on as a substitute for Dražen Ladić in the 29th minute.
Prior to the UEFA Euro 1996 finals, he appeared in three friendly matches, also playing the full 90 minutes in a goalless draw against England at Wembley. During the finals, he was Croatia's second-choice goalkeeper, with Dražen Ladić being the first choice, and made his only appearance in their final group match, a 3–0 defeat to Portugal.
He went on to make three appearances in the 1998 FIFA World Cup qualifying, which included playing the full 90 minutes in the second leg of the playoffs against Ukraine. He was also part of the 22-man squad that won the bronze medals at the 1998 FIFA World Cup finals, but did not make an appearance during the tournament.
In January 1999, he won his only international cap for Croatia B in a friendly match against France B. He also continued to be Croatia's second-choice goalkeeper during the UEFA Euro 2000 qualifying. His only appearance in the qualifying came in a 2–1 win at home to Malta on 21 August 1999. It eventually turned out to be his final international appearance, as he retired from international football two months later, following Croatia's failure to qualify for the finals.
- "Statistika: Marjan Mrmić" (in Croatian). Hrvatska nogometna liga. Retrieved 2009-10-12.
- "PREDSJEDNIK TUDJMAN ODLIKOVAO HRVATSKU NOGOMETNU REPREZENTACIJU" (in Croatian). hrt.hr.