Munro was born in Uddingston and began his career at St. Mirren making 103 league appearances for the Buddies in four years scoring 16 goals before moving to Hibernian in 1973. He spent three years at Hibs playing in 61 league matches and then joined Rangers for a short spell before making a return to Love Street. Munro spent three years back at St. Mirren before moving south to Stoke City where he spent the 1980–81 season making 34 appearances scoring once which came in a 2–1 away victory at Southampton. In the summer of 1981 manager Alan Durban moved to Sunderland and he took Munro up to Roker Park with him. He spent three seasons at Sunderland making 88 appearances and later played with Dundee United and ended his career with a second spell at Hibernian.
He is currently YSC Director and Union Youth Director at YSC Sports in Wayne, Pennsylvania, USA, a youth soccer center which aims to provide high quality coaching for kids with an aim of developing skills in young players. YSC is the official youth development partner of the Philadelphia Union, a Major League Soccer club. Munro also does half-time television commentary for the Union's home games.