Málek made his first professional start at 16 years old on January 30, 2019, for VHK Vsetín of the second-tier Czech Chance Liga against HC Stadion Litoměřice, but was pulled midway through the match after conceding four goals.[1]
Returning to the Chance Liga more permanently in the 2020–21 season, Málek recorded 8 wins and a .912 save percentage in 14 games. In 7 playoff games, he recorded a .927 en route to a semifinal exit at the hands of HC Dukla Jihlava. In 21 total games at the Chance Liga level, he recorded two shutouts.[2][3] Despite not being ranked at all by NHL Central Scouting, he would be selected 100th overall in the fourth round of the 2021 NHL entry draft by the New Jersey Devils.[4]
On October 20, 2021, early in the 2021–22 season, Málek became the first goalie in Chance Liga history to score a goal by shooting the puck directly into the net (as opposed to being credited with a goal he didn't directly score) when he scored an empty-net goal late in a 4–1 victory over AZ Havířov.[5] He would play 31 games that season and post 22 wins, two shutouts, and a .932 save percentage, earning the league award for best goaltender and making a run to the Chance Liga finals.[6]
Moving to Finland for the 2022–23 season, Málek signed a two-year contract with Ilves of the top-level SM-liiga on May 3, 2022.[7] Early in the year, Málek was hospitalized for panic attacks caused by what he described as putting too much pressure on himself.[8] After recovering, as well as some time playing in the second-tier Mestis, he returned to Ilves and finished the season with a .903 save percentage in 22 total games.[9][10] In the playoffs, starting goaltender Marek Langhamer was unable to play midway through the semifinal series against the Lahti Pelicans, thrusting Málek into the starting role.[11]
On March 6, 2024, Ilves exercised an option in Málek's contract to sign him to a one-year extension.[12] On May 6, 2024, Málek signed a two-year, entry-level contract with the Devils.[13]
Málek is a supporter of the Forest Green Rovers football club. He initially discovered the team while playing EA Sports FIFA and is a fan of their environmentally conscious operations.[5]