István Molnár was a swimmer and water polo player for Ferencváros from 1932 and Budapesti Vasas from 1945. He achieved his best international level results in water polo. He won a league title with both teams, with Ferencváros in 1944 and Vasas in 1947. From 1934 to 1944 he appeared ten times in the Hungarian national team. At the 1936 Berlin Olympics he was a member of the Hungarian team that won the gold medal. In the tournament he only appeared in the match against Malta, so as a member of the Kutasi, Molnár, Tarics trio (the three of them only appeared in this match) he jokingly became the “Knight of Malta”. He was also a member of the team that won first place at the 1938 European Championship in London. He retired from active sports in 1947.
From 1934, he was the secretary of the National Sports Swimming Pool, and after the Second World War, he was a lecturer at the OTSH (National Physical Education and Sports Office). From 1961 he was a water polo instructor at MTK and in 1962 he became an employee of Fővárosi Elektromos Művek. In the meantime, he also worked as an announcer at the Népstadion (the main stadium in Budapest) from 1953 until his death.