Martinas Geben was a Žalgiris player between 2018 and 2021, and spent the first season as a player on loan at Juventus Utena. At the end of the season, which he finished with an average of 11.5 points, 7.4 rebounds and 1.2 blocks per game, he was also selected as the Most Valuable Player of the Lithuanian national championship. He moved to Bamberg in 2021, and started the 2022/23 season with the Skyliners from Frankfurt and finished with Manresa, where he played until the end of last season.

With Žalgiris, he won the title of national champion of Lithuania in 2020, and in the 2019/20 and 2020/21 seasons, he also played in a total of 53 Euroleague games for Žalgiris. He averaged just over eight minutes per game, averaging 3.4 points and 2.0 rebounds per game.

In the 2023/24 competitive season, he played in 34 ACB League games with Manresa, averaging 8.4 points and 4.1 rebounds per game. He also played in the Basketball Champions League with Manresa in the 2022/23 season, where he appeared in eight games and averaged 7.3 points, 4.3 rebounds and 1.4 assists.

Geben is also an occasional member of the Lithuanian national team, with whom he played in the 2019 and 2023 World Cup qualifiers, as well as in the 2025 EuroBasket qualifiers. He won a bronze medal with Lithuania at the 2013 Under-19 World Championship.