After starting his career at FC Volendam, Mühren moved to Ajax Amsterdam in 1971. He had his first domestic success with FC Twente, winning the KNVB Cup in 1977. A year later he moved to Ipswich Town in England for a fee of £150,000; in the same year he made his international debut in a 4–0 win against Tunisia. He was part of the successful Ipswich team that won the 1981 UEFA Cup. In 1982 he transferred to Manchester United. He helped United win the 1983 FA Cup Final by scoring a penalty in the replay, and left the club after the 1985 FA Cup Final, in which United defeated Everton. He did not feature in the match squad for the 1985 final.
He was one of the few players from outside the United Kingdom and Ireland playing in English football in that era.
After his stay in England, Mühren returned to Ajax, where he added the European Cup Winners' Cup (1986–87) to his trophy collection. At the age of 37, he achieved the highlight of his career, when he was a vital part of the Dutch national team that won the European Championships in 1988. In the final against the Soviet Union he provided the cross from which Marco van Basten scored the second goal (considered one of the greatest volleyed goals of all time). He continued playing for Ajax for one more season after that, finally hanging up his boots in 1989 at the age of 38.