- 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. 
He hit .320/.427/.660 for Kotlarka Praha in 2019, with 29 runs, 9 homers and 30 RBI in 27 games. In the postseason, he batted .377/.467/.675 with 19 runs in 20 games. He tied Terrell Joyce for the most homers in the regular season, was 7th in RBI, tied Jakub Sládek for 7th in extra-base hits (17), was 7th in total bases (68, between Hejma and Trey Bridis) and tied Jerry Lacayo for the most times plunked (11).  In the 2019 European Championship, he hit .310/.394/.404 while starting in left (he had 10 putouts and no errors); most notable was the winning homer off Belgian's Kenny Vandenbranden.  The Czechs won a spot in the 2019 Europe/Africa Olympic Qualifier. In that event, he had a six-RBI day against South Africa, with a grand slam off Dean Jacobs, and drove in their only run against the Netherlands. For the event, his batting line was .316/.381/.474 with seven RBI in five games. He finished third in the event in RBI, behind former major leaguers Danny Valencia and Chris Colabello. 
The 24-year-old produced at a .423/.472/.817 clip between the regular season and postseason in 2020, with six triples, eleven homers, 41 runs, 51 RBI and 13 steals in 15 tries over 34 games. He led the league in hits (two ahead of Radim Novotný), average (.010 ahead of Jakub Kubica), triples (double runner-up Michael Vykoukal), extra-base hits (28, 8 ahead of Jakub Voják), total bases (116, 38 ahead of runners-up Marek Chlup and Vykoukal), homers (tied Matěj Menšík) and RBI (16 ahead of #2 Jakub Grepl and Voják). He was also 5th in OBP (between Voják and Čech), second in slugging (.042 behind Menšík), second in OPS (15 behind Menšík), tied Arnošt Dubový for second in runs (8 behind Kubica) and 3rd in doubles. 
In 2021, he moved to Sokol Hluboká and batted .354/.455/.696 with 41 runs, 35 RBI and 13 homers in 42 games, stealing 19 bases in 22 tries. He was among the leaders in numerous categories: homers (2nd, one behind Marek Minařík), RBI (7th), hits (56, 6th), slugging (4th, between Tyler Smith and Eugene Helder), OPS (5th), runs (tied Dubový for 5th), steals (2nd, one behind Ondřej Blažka), doubles (tied Pavel Budský for 5th), triples (2, tied for 5th), extra-base hits (26, 1st, 2 ahead of Minařík), total bases (110, 2nd, one behind Minařík) and hit-by-pitch (9, 3rd).  He was back with the Czechs for the 2021 European Championship, starting at first. He handled 37 chances error-free and hit .231/.333/.308. 
Martin batted .358/.444/.701 in 2022. He was 7th in homers (6, between Menšík and Keibert Petit), 7th in average (between Dubový and Martin Červinka), 8th in OBP, 4th in slugging (between Helder and Pabel Manzanero) and 4th in OPS (between Helder and Manzanero).  Despite being only 26 years old, he was among the league's career leaders in homers (78, 6th, between Malík and Roman Talda) and extra-base hits (163, 16th, between Tomáš Juněc and Jakub Hajtmar) as well as a couple rate stats: slugging (8th, between Tomáš Přibyl and Matthew Lawman) and OPS (8th, between Tomáš Přibyl and Wayne Ough).  He homered off Armando Dueñas Jr. of Spain in the 2022 World Baseball Classic Qualifiers. In the rematch with Spain, he came up even bigger, with a two-run shot off Ronald Medrano that was the winning hit in a 3-1 victory. That put the Czechs in the 2023 World Baseball Classic, their first World Baseball Classic. He hit .267/.353/.667 with four RBI in four games. Only Harry Ford hit more homers in the tournament and he tied for 10th in RBI. 
- 2013 European Junior Championship
- 2013 World Junior Championship
- Extraliga site; all Extraliga stats listed are from this site
- 2014 European U-21 Championship
- 2016 European Champions Cup
- Wake Tech bio
- Wake Tech release
- 2017 European U-23 Championship
- Wake Tech
- 2018 Super6
- 2019 European Championship
- 2019 Europe/Africa Olympic Qualifier
- 2021 European Championship
- Baseball-stat.cz career leaderboards
- WBC Qualifiers