After starting his career at FC Volendam, Mühren moved to Ajax Amsterdam in 1971, winning 3 domestic and 3 international titles in his first two seasons there. His third season with Ajax yielded no titles, but he found further success after a transfer to FC Twente, winning the KNVB Cup in 1977 and reaching the 1975 UEFA Cup Final. 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, and finished second in the league that year and the year after. In 1982, he transferred to Manchester United. He helped United win the 1983 FA Cup Final by scoring a penalty in the replay against Brighton, 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, having lost his place in the team that season to new signing Jesper Olsen.