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.

His NHL career began in 1991. His first NHL team was the San Jose Sharks, he played with them from 1991–92 to 1995–96. With Irbe between the pipes, the newly established Sharks made their first playoff appearance in the 1993–94 season and upset the top-seeded Detroit Red Wings. That season, Irbe played an NHL record 4412 minutes in goal for the Sharks. Irbe, affectionately known as Archie, was nicknamed “The Wall” and became a cult figure in San Jose, a status he enjoys there to this day. Following an injury (his hand being mauled by his pet dog in the offseason) and a poor 1995–96 season, Irbe was released by the Sharks.

After a disappointing 2002–03 season, the Hurricanes looked to demote Irbe because they could not move him because of a no-trade clause in his contract. On October 16, 2003, Irbe was assigned to the Johnstown Chiefs of the ECHL. After going 8–2–1 in 11 games with the Chiefs, Irbe was named as the starter for the Eastern Conference in the 2004 ECHL All-Star Game. However, Irbe was unable to participate due to a wrist injury. On March 19, 2003, Irbe was recalled to the Carolina Hurricanes after goalie Kevin Weekes was placed on the IR due to season-ending hand surgery.

In June 2004, he was traded to the Columbus Blue Jackets, but never played with the club due to that year’s NHL Lockout. After the lockout that canceled the 2004–2005 season, Irbe never played in the NHL again but chose to continue his career in Europe.

At the 2006 Winter Olympics in Turin, Irbe was Latvia’s flag-bearer in the opening ceremonies.

In 2008, Irbe signed a three-year deal with Dinamo Riga and worked as the goaltending coach for the club. In August 2009, Irbe cut ties with Riga and decided to go back to North America to be the goaltending coach of the NHL Washington Capitals after former goaltending coach Dave Prior stepped down due to family reasons. Irbe left the team on June 11, 2011 to spend more time with his family.

In 2013, Irbe was named as Ted Nolan’s assistant for Latvian national team, but resigned a year after a dispute with president of Latvian Ice Hockey Federation Kirovs Lipmans over his coaching certification. In August 2014, Nolan again hired Irbe as an assistant, this time with the Buffalo Sabres.

In August 2017, Irbe became consultant for Latvian hockey league club HK Kurbads.