Born in Vorkuta, USSR, Andrei Nikolishin played domestically for Moscow Dynamo. In 1992 he helped the Commonwealth of Independent States win the gold medal at the World Junior Championships in Germany. The next year, he helped Russia win gold at the World Championships and was also on hand in 1994 for the Lillehammer Olympics and World tourney. Following the 1993-94 domestic and international season, Nikolishin was named to the CIS First All-Star Team and was voted the Player-of-the-Year in his country.
A second round draft pick of the Hartford Whalers in 1992, the talented forward joined the NHL after the owners' lockout in January 1995. He adjusted to the North American style of play and was used on both the power play and shorthanded situations. In 1995-96 Nikolishin registered 51 points then joined Russia at the World Championships after Hartford missed the playoffs.
After scoring four points in as many games for Russia at the World Cup in 1996, Nikolishin began the 1996-97 season in Hartford but was traded to Washington in November for defenceman Curtis Leschyshyn. He played solidly for his new club and represented Russia at the 1997 World Championships. During the 1998 playoffs the creative winger registered 13 assists to help the Caps reach the Stanley Cup finals. After a brief contract holdout in 1998-99, he rejoined the Caps and was an excellent checker and special teams player.
By the 1999-00 season, Nikolishin was considered one of the top penalty killers in the NHL and represented his homeland yet again at the World Championships. The next year he was used on offense a bit more because of his fine playmaking talents. Nikolishin figured to be an important part of the free flowing style of the club in 2001-02, especially after the Capitals acquisition of Jaromir Jagr.
After a strong 2001-02 season which saw Nikolishin capture a bronze medal at the 2002 Salt Lake City Olympic Games, he was dealt to the Chicago Blackhawks prior to the 2002-03 season. Nikolishin's stay in the Windy City lasted only one season as he was dealt to the Colorado Avalanche in the summer of 2003.