Ján Mucha started his career in his local club TJ Slovan Belá nad Cirochou. Then he moved to MŠK Snina, and later to Inter Bratislava. He spent there 2 seasons in A-team, but he did not play in any match. He moved to MŠK Žilina in summer 2002 and won the Slovak championship there twice. In January 2005, he was sent on a half-year loan to Humenné.
He signed for Legia Warszawa in summer of 2005. For the first two years at Legia he was second-choice goalkeeper, behind Łukasz Fabiański, until Fabiański moved to Arsenal in the summer of 2007. For the next three years Mucha was Legia's first-choice keeper and consistently excelled in this position. He won the 2007–08 Polish Cup and the Polish Supercup in 2008. In the summer of 2010 his contract ran out and on the back of an excellent season he signed for Everton on a free.
In January 2010, Mucha signed a pre-contract deal with English Premier League club Everton to join them on 1 July. On 4 August 2010, Mucha made his Everton debut playing the first 45 minutes of a pre-season friendly against Chilean side Everton de Viña del Mar at Goodison Park, before being replaced in goal by Iain Turner at half-time. His competitive debut for Everton came in the first match of their League Cup campaign, a 5–1 win over Huddersfield Town. He went on to play in the successive League Cup match against Brentford, in which he saved a penalty kick in the second half, but could not keep his side in the competition in the penalty shootout to decide the match, which Everton lost 4–3. Mucha made his sixth appearance for the club and his first in the 2012/13 season in a League Cup tie at home to Leyton Orient in August 2012, which Everton won 5–0. Mucha played in the next round as Everton lost 2–1 away to Leeds United. So far, all of his appearances for Everton have come in this competition.
Mucha made his debut for Slovakia in February 2008, in a friendly match against Hungary, and became the national team's first-choice goalkeeper. When Slovakia qualified for the FIFA World Cup for the first time, in 2010, Mucha played in all four games as Slovakia made it to the second round of the competition. On 8 October 2012, Mucha has retired from international football with immediate effect.
- 2003, 2004