Irbe was drafted in the 10th round, 196th overall by the Minnesota North Stars in the 1989 NHL Entry Draft.
His first professional hockey team was Dinamo Riga of the Soviet Hockey League (from 1987 to 1991). After playing in only 2 games during the 1986–1987 season Irbe got a chance to become Dinamo Riga's number one goaltender during the 1987–1988 season when their starting goaltender and Olympic champion, Vitali Samoilov went down with a long term injury. In his only full professional season, Irbe was outstanding in helping Dinamo Riga make it to the finals of the Soviet Hockey League where they eventually lost to perennial Soviet champions CSKA Moscow. During this period he also played for the Soviet Union in the World Championships in 1989 and 1990. The Soviet team won those two championships and Irbe was honoured as the best goalkeeper of the 1990 tournament. He refused to play for the Soviet Union in 1991 because Latvia had proclaimed independence from the Soviet Union on 4 May 1990 and the Soviet government attempted to use military force in January 1991 to stop Latvia's independence. When the Moscow government sent tanks rolling to Riga, Irbe was among those who took to the streets and put up barriers to protect buildings, radio stations, TV towers and historical landmarks.