After playing with TJ Vitkovice Jr. in the Czech junior league, Malík was drafted 72nd overall by the Hartford Whalers in the 1993 NHL Entry Draft. He played one season for HC Vítkovice of the Czech Extraliga before joining the Whalers' American Hockey League affiliate, the Springfield Falcons, in 1994–95. He played the better part of two seasons with the Falcons before earning a roster spot with the Whalers. Marek scored his first career NHL goal on October 19, 1996 against Jeff Reese and the New Jersey Devils in a 6-2 Whalers victory. While the Whalers' franchise relocated to Raleigh, North Carolina in 1997–98 to become the Carolina Hurricanes, Malík played in the SwedishElitserien with the Malmö Redhawks. He returned to the NHL the following season with the Hurricanes. In 2001–02, Malík recorded a career-high 23 points. The following season, his ninth with the Whalers/Hurricanes franchise, Malík was traded to the Vancouver Canucks along with Darren Langdon in exchange for Jan Hlaváč and Harold Druken. He completed his second season with the Canucks, in 2003–04, as co-recipient of the NHL Plus/Minus Award with a +35 rating. During the 2004–05 NHL lockout, Malík returned to the Czech Extraliga to play for HC Vítkovice. With NHL play set to resume the following season, he signed a three-year deal with the New York Rangers. On November 26, 2005, Malík scored on Washington Capitals netminder Olaf Kölzig to finish the then longest shootout in NHL history. The goal was described as a "circus shot" as Malík drew the puck towards the center of the net, put his stick between his legs, and shot high on Kölzig's stick side. With goalies Henrik Lundqvist and Kölzig dominant in net, the shootout went to 15 rounds. The teams had selected so many players to shoot that they were being forced to send out their weaker defencemen. Bryan Muir of the Caps scored in round 14, and Jason Strudwick answered for the Rangers to tie the score again. The next Caps shooter was stopped by Lundqvist, which set the stage for Malík. He skated in on Kölzig, deked to his glove, pulled the puck back, put his stick through his legs, and flipped the puck in over Kölzig's blocker to score and win the game. He had not scored a goal during the season at the time. After the shot, he raised his arm and shrugged to the fans before being mobbed by his teammates. Former Rangers commentator John Davidson said, "Now I've seen it all! First Strudwick scores, then Malík wins a shootout with a shot between the legs. Oh Baby!" The goal was ranked as the play of the year by TSN's SportsCentre. During his time with New York, Malík was criticized for his lack of physical play, despite his size, as well as his risky decision-making with the puck. These criticisms have been applied to Malík as early as his minor league days in Springfield. On January 24, 2008, he was not at the game on Brian Leetch Night, even though it was team policy for players to be present at games. He also did not attend practice and his locker was empty for the game after he refused to shake hands with head coachTom Renney after a victory in the Rangers' previous game. On October 14, 2008, Malík signed a one-year contract with the Tampa Bay Lightning. On November 23, 2009, Malik signed a one-year contract with the Genève-Servette HC from the Swiss National League A. On May 7, 2014, Malik announced his retirement.
Malík has a wife and two sons. Malik's teammates and coaches called him "Harry", a nickname he received during his rookie season in Hartford because he reminded them of the title character from Harry and the Hendersons.
