 Born in Kherson, Ukrainian SSR, Soviet Union, Maksymov played for Valery Lobanovsky's Dynamo Kyiv in his native Ukraine, before transferring to SV Werder Bremen and SV Waldhof Mannheim in Germany.Whilst at Werder Bremen he helped them win the 1998–99 DFB-Pokal, starting in the final against Bayern Munich as Bremen won on penalties.Maksymov had earlier scored in the game for Bremen as it finished 1-1 before the shootout.