Munro started his career as a centre-forward with Chelsea at junior and amateur level in 1961–62, after leaving school, but he left without signing professional forms. Following this, he returned home to his native Scotland and signed as a professional for Dundee United. He broke into the first team in 1964 and won four Scotland youth caps during his time at Tannadice. In October 1966, he moved to fellow Division 1 outfit Aberdeen for £10,000. His first season proved a success as he collected a runners-up medal as the team fought its way through to the 1967 Scottish Cup Final, losing 0–2 to Celtic at Hampden Park. This was sufficient to qualify for Europe though, and they competed in the Cup Winners' Cup the following season, giving Munro his first – but not last – taste of European football. Munro scored Aberdeen's first goal in European competition, in a 10–1 win against KR Reykjavik. In the summer of 1967, Munro and Aberdeen travelled to America to compete in the newly formed United Soccer Association league. Due to the lack of existing teams, the league organisers instead imported several established teams from around the globe to compete under 'franchise' names. Aberdeen competed as the "Washington Whips", based in the capital. The Whips won the Eastern division and so progressed through to the championship play-off match in July, where they faced the Western champions, Los Angeles Wolves. The Whips eventually lost 5–6 in extra time, but Munro's performance in scoring a hat-trick, caught the eye of the oppositionmanagerRonnie Allen.
Wolverhampton Wanderers
In October 1968, Wolves acted upon this display and signed Munro for £55,000. Munro went on to play 371 times in total for the club, becoming firmly established at centre back, despite signing as a midfielder. He also chipped in with 18 goals in total, including scoring in both legs of the 1972 UEFA Cupsemi final defeat of Ferencváros and played in the final, collecting another runners-up medal after a 2–3 aggregate defeat to Spurs. Munro didn't have to wait too long though for a winners' medal as Wolves lifted the 1974 League Cup, after a 2-1 victory over Manchester City at Wembley. The Wolves also won the Texaco Cup in 1971. His performances for Wolves also won him nine Scotland caps – as well as four at under-23 level – spread from 1971 to 1975. His full debut coming on 18 May 1971 against Northern Ireland. His last appearance for Scotland was in a 1–1 draw against Romania in Bucharest. Shortly after helping the Midlanders to regain their First Division status in 1976–77 — after a year outside it – Munro returned to Scotland when the lure of Celtic proved too strong. He signed after a short loan period in December 1977 for £20,000. Munro was the last player Jock Stein signed as Celtic manager.
Later life
Stein saw Munro as being a replacement for the injured Pat Stanton. His time in Glasgow was to prove short-lived, however. Despite picking up another runners-up medal, Celtic only finished fifth in the Scottish Premier Division. Munro was released by Celtic in the summer of 1978 and he headed for a new challenge in Australia by signing for South Melbourne Hellas, managed by former Wolves goalkeeper Dave MacLaren. Although initially this was only planned as a short-term arrangement, he ended up moving there permanently. During the 1980s Munro took up a player/coach role at Albion Rovers, before retiring as a player. He later managed Hamlyn Rangers and Keilor Park. He returned to the UK in 1991 and settled in Wolverhampton, with his partner Naomi. He suffered a stroke in the early 2000s that left him confined to a wheelchair for his remaining life. He died on 16 August 2011 after suffering acute breathing difficulties.