Moon was born in Perth Royal Infirmary on 8 June 1987.
Moon was a bright talent, and played for local boys' club team Bankfoot Boys' Club, playing two age groups above himself, lining up alongside his older brother Stephen. However, as the team progressed, so did Moon, so he moved to Fife boys' club Fossoway.
Moon was a pupil of Luncarty Primary School and Perth Grammar School.
Moon had played at youth level for St Johnstone and was a big part of the very successful under-17 side in the 2003–04 season, and that prompted then-manager John Connolly to give Moon his first professional contract in the summer of 2004. Other players given deals that summer included Andy Jackson and Neil McCallum.
Moon made his professional debut in a Scottish League Challenge Cup tie against Raith Rovers at McDiarmid Park during the 2005–06 season. He came on as a substitute after 60 minutes, and was impressive and the side went on to win 5–1. Having been a St Johnstone fan all his life and being well known as the "local hero" by many of the clubs fans, Moon gained the nickname "Mooner" and a chant was introduced, and he is widely known as a fans favourite. Despite injuries ruining his second season, Kevin managed to make one more appearance from the bench during the 2005–06 campaign.
The 2006–07 season saw Moon in a difficult situation, where he was too old to play for the under 19s, but not yet regarded as a first team player, and for that reason manager Owen Coyle sent Kevin on loan to Forfar Athletic, originally for 6 months, however the loan was extended on 31 December 2006 to run through until the end of the season.
After a successful loan period at Forfar, Coyle rewarded Moon with a new one-year contract. The start of the 2007–08 campaign wasn't great for Moon, after a couple of niggling injuries he never managed to force himself into recognition for a first team spot. However, his big break came when manager Owen Coyle, and his assistant Sandy Stewart, left St Johnstone to join English Football League Championship side Burnley, and Moon's team mate Derek McInnes was appointed as player/manager until the end of the season. Upon being appointed as manager, McInnes revealed to the local press that he was a big admirer of Moon's talents, and showed this by giving him his first league start away to Clyde at Broadwood Stadium on 29 December 2007, where Moon capped off a man of the match performance with a late goal. St Johnstone won 3–1. He scored his second goal for the club after coming off the bench against Stirling Albion at McDiarmid Park in January 2008, his goal meant that St Johnstone won the game 2–1. Moon made 7 starts, and 14 appearances from the bench during the campaign, scoring three times.
McInnes gave Moon a new one-year deal in May 2008, with the view to an extension if he impressed during the 2008–09 campaign and in the January, Moon penned a new contract with the club that will tie him to Saints until May 2011. So far he's made a numerous appearances, a few starts but mostly off the bench. Moon started a game at East End Park against Dunfermline Athletic in November 2008, where after 20 minutes, Stephen Glass made a late tackle on Moon in which he studded Kevin's diaphragm. This caused Moon to stop breathing, and lose consciousness. He was rushed to hospital, but regained consciousness before he left the ground. After this small setback, Moon started again at Dens Park against rivals Dundee also in November. Moon played an integral part in St Johnstone's promotion to the SPL, particularly whilst Jody Morris was out of the side injured.
Moon started off his SPL season in good form, and scored his first top flight goal with a late equaliser against Dundee United at Tannadice. However, in March 2010 in a midweek clash with Aberdeen, Moon was badly injured in a clash with midfielder Mark Kerr, and was stretchered off having played a massive part in St Johnstone victory by then. At first, it was reported that Moon had damaged his medial ligament and would be back within 4–6 weeks, however, following further scans it was discovered that Moon had torn his cruciate ligament and would be out for 6 months. He made some appearances near the end of the 2010–11 season after returning from injury. Moon was then given a short term contract to further prove his fitness. He became a first team regular in the early part of the 2011–12 season and was given an extended contract by new manager Steve Lomas. The 2012/13 season has been one of frustration for Moon, who has found himself isolated by current manager Steve Lomas.
Moon went to Forfar on 31 August 2006 originally the deal was until 31 December 2006, however it was extended until 15 May 2007. Moon made 25 appearances for Forfar Athletic, 23 starts and 2 sub-on appearances, netting twice. He was voted Players' Player of the Year and Fans' Player of the Year at the end of season awards, and despite being a great success, Moon couldn't prevent them from being relegated to the Scottish Football League Third Division.
Alloa Athletic manager Paul Hartley signed Moon in February 2013 after he was released by St Johnstone. Moon has signed with 'The Wasps' until the end of Season 2012/13.
Moon signed for Raith Rovers on 28 May 2013 on a one-year deal. He was part of the Raith Rovers side which beat Rangers in the final of the Scottish League Challenge Cup in the 2013-14 season.
Moon signed a one-year deal with ECU Joondalup SC and made his debut for the club in the 3-0 win against Sorrento in June 2016. Moon signed for another year at the end of the season, after he helped turn the clubs fortunes around as they narrowly missed out on the title.
Moon currently resides in Perth, WA, with his current teammate Gordon Smith. Moon and Smith were also teammates during their time at Raith Rovers.