Born in
Copenhagen, Molnar played football in Copenhagen clubs
B 1908,
Fremad Amager and
Hvidovre IF. Molnar's talent was acknowledged, as he played seven games and scored four goals for the Danish under-19 youth national team from 1986 to 1988. He made his senior debut in 1987 for Hvidovre in the
Danish 2nd Division, before moving to play
semi-professionally for top-flight club
Boldklubben Frem in 1989. Molnar got his senior level breakthrough when he became joint top goalscorer of the
1989 Danish 1st Division championship with 14 goals, as Frem finished eighth of 14 teams. He was selected for the
Danish under-21 national team in June 1989. Several clubs were interested in buying Molnar, including Danish club
AGF, English club
Chelsea, French club
Olympique Lyonnais and
Standard Liège from Belgium. He moved from Liège to Swiss club
Servette FC in the summer 1991. Molnar became league top goalscorer, as he scored 18 goals in 34 games for Servette in the Swiss
1991–92 Nationalliga A championship. Molnar was an integral part of the Danish under-21 national team from 1991 to 1992, forming a successful attacking partnership with
Peter Møller. Molnar played all Denmark's games from the qualification to the semi-finals of the
1992 UEFA European Under-21 Football Championship, which qualified Denmark for the 1992 Summer Olympics in
Barcelona. He was named 1991
Danish under-21 Player of the Year. Molnar played all of Denmark's three games at the 1992 Olympics final tournament, but was
sent off for a physical scuffle with a defender in Denmark's final game before elimination against the
Australia under-23s. He ended his under-21 career after the 1992 Olympics, having scored a total eight goals in 21 caps. Having ended his loan at Servette, Molnar looked to find a new club in the summer 1992. Molnar was bought by French club
AS Saint-Étienne for
FRF 6.000.000. He did not fit into Saint-Étienne's technical short passing tactics, and did not find goalscoring success at the club. He was released from his contract in January 1994, and moved back home to Denmark. In February 1994, he agreed to play for
Lyngby BK in the top-flight Danish championship, now called the
Danish Superliga. With the stated ambition of moving abroad, Molnar played half a year at Lyngby, but did not get along with Lyngby manager
Michael Schäfer. He moved to German club
FSV Frankfurt in September 1994. Despite scoring 12 goals in 20 games in the
1994–95 German 2nd Bundesliga season, Molnar could not keep Frankfurt from
relegation into the lower
Regionalliga division. Molnar went home to Denmark, and started playing for Superliga club
Herfølge BK in September 1995. When Lyngby's first-choice striker
David Nielsen left the club in June 1996, Molnar moved back to his old club to fill the spot. He was the leading goal scorer in the
1996–97 Danish Superliga with 26 goals in 33 games, and was recalled to the Danish national team by new national manager
Bo Johansson, after a hiatus of more than five years. After three goals in five games at the start of the
1997–98 Superliga season, Molnar was sold to Spanish club
Sevilla FC in the secondary
Segunda División league, where he joined fellow Danish international
Thomas Rytter. In his first year at Sevilla, Molnar scored ten goals in 27 games, and he was included in the Danish squad for the
1998 World Cup. He took part in one match at the tournament, when he most remarkably came on as a substitute in the 58th minute of the 1–1 draw with
South Africa, only to be
sent off eight minutes later. His second season at Sevilla was not as successful, and Molnar was dropped from the team. When visiting
American international midfielder
Chris Henderson in
Colorado, a former teammate of his, Molnar had been fascinated by the atmosphere in the American
Major League Soccer (MLS) championship. In January 2000, he moved to MLS to play for
Kansas City Wizards. While at the Wizards, he was included in the Danish squad for the
2000 European Championship in June 2000. He played a single match at the tournament, before ending his national team career. He retired from football in October 2000, after scoring the game-winning goal during the
2000 MLS Cup, as the Wizards beat
Chicago Fire 1–0. On 2 October 2011, he got a comeback, playing 20 minutes for his childhood-club,
B1908, in a
2nd division game. ==Honours==