Finnur won 15 caps and scored two goals for Iceland at youth level and won a single cap for the senior team, as a late substitute for Baldur Þór Bjarnason in a 1–0 friendly defeat to the United States on 31 August 1993.

A midfielder, Finnur made 287 appearances and scored 36 goals across three spells for Fylkir in his native Iceland between 1989 and 2005. He won the Icelandic Cup and three 1. deild karla championships with the club. Earlier in his career he also played in Malta and Belgium for Hibernians and KSV Bornem respectively.

Finnur Kolbeinsson (born 21 March 1972) is a retired Icelandic semi-professional football midfielder who made over 200 appearances for Fylkir. He also played in Malta and Belgium and was capped by Iceland at international level.