Obšut was drafted to the National Hockey League (NHL) in 1995 by the Winnipeg Jets in the eighth round, 188th overall. Obšut played seven games in the NHL, four for the St. Louis Blues and three for the Colorado Avalanche. After playing with Luleå in the Swedish Elitserien for five seasons, Jaroslav signed a two-year contract with HC Spartak Moscow of the Kontinental Hockey League on May 27, 2009. During his second year with Spartak, Obsut was released to play with league rival, HK Atlant, on November 26, 2010.