- Bats Right, Throws Right
- Height 6' 0", Weight 205 lb.
- School Wake Technical College
He attended the MLB European Academy in 2013.  He hit .235/.263/.294 in the 2013 European Junior Championship while playing error-free ball at catcher.  He was 0 for 14 with a walk in the 2013 World Junior Championship.  He made his Extraliga debut in 2014 with a bang for Kotlářka Praha, going 7 for 16 with two doubles and a homer.  He was 0 for 3 in the 2014 European U-21 Championship. 
For Kotlářka Praha in 2015, he batted .294/.350/.505 with 8 doubles and 5 homers in 109 at-bats. He was 2 for 15 with a walk and two runs in the 2016 European Champions Cup.  He had a superb Extraliga campaign at .344/.438/.739 with 15 homers, 49 runs and 49 RBI in 38 games. He tied Michal Zýma for 3rd in the league in runs, tied for 6th in hits (54), tied for 6th in doubles (11), tied Australians Mitch Nilsson and Ryan Battaglia for the most dingers, tied for 4th in triples (3), was 3rd in RBI (after Matěj Hejma and Nilsson), was 4th in hit-by-pitch (8), was 3rd in slugging (behind Hejma and Martin Schneider) and was 5th in OPS (between Petr Síla and Nilsson).
He came to the US for college ball in 2016-2017, hitting .406/.482/.744 for Wake Technical College, with 22 doubles, 50 runs, 47 RBI and 14 steals (in 17 tries) in 48 games.  He was named second-team NJCAA second-team All-American.  He kept on rolling in the 2017 European U23 Championship, with a batting line of .579/.704/1.263, 13 RBI and 7 runs in 6 games. He led the event in average, OBP, slugging, RBI, homers (3) and total bases.  Returning to the Extraliga after Wake's season ended, he hit .341/.389/.695. he was 9th in the loop in average, 2nd in slugging (.070 behind Hejma), 2nd in OPS (behind Hejma) and tied Daniel Vavruša for 6th in homers (despite playing about a third as many games as Vavruša).
Mužík was even better his second year at Wake, hitting .407/.497/.793 with 48 runs and 56 RBI in 45 games. He again was second-team All-American.  He then finished the year back in the Extraliga, producing at a .337/.449/.571 clip there. He was 7th in slugging, between Jakub Malík and Petr Čech.
Martin then made his debut with the Czech national team, putting on a show at the 2018 Super6. He singled off Orlando Yntema in his first at-bat and later had a 6-RBI game against Belgium, including a 3-run bomb off Robbe De Jongh. He tied Robel Garcia for 6th in the event with 7 RBI and tied for 3rd with 4 walks in 5 games. He led the Czechs in average, was second to Malík in slugging and second to Čech in OBP; he hit .385/.526/.692.