Europe Beginning in 2000–01, Kostitsyn spent the first two seasons of his early career with
Polimir Novopolotsk, competing in several leagues, including the
Eastern European Hockey League (EEHL). In the summer of 2002, he signed with
CSKA Moscow and moved to
Russia. He split his time with the organization between CSKA 2 of Russia's developmental league, and also continued to play in the Belarusian league with
Yunost Minsk. After his first season with CSKA, he was selected by the
Montreal Canadiens in the first round, tenth overall, of the
2003 NHL entry draft. Kostitsyn drew favourable scouting reports from his strong showing at the
2003 World U-18 Championships and was expected to be taken even higher in the draft; it is speculated that health concerns with his back caused teams to pass him over. He was subsequently assigned to the Canadiens'
American Hockey League (AHL) affiliate, the
Hamilton Bulldogs, for the
2004–05 season. He scored his first goal with Hamilton in his first game, on 15 October 2004, and finished the season with 23 points in 66 games. Midway through the
2005–06 season, he was called up by the Canadiens and played his first
National Hockey League (NHL) game on 1 December 2005, but was limited to just one shift in a 3–2
overtime loss to the
Buffalo Sabres. He was called up again later in December and scored his first career NHL goal on 13 December against
Curtis Joseph in a 5–2 win over the
Phoenix Coyotes. Kostitsyn had a breakout season in
2007–08, playing on the Canadiens' most productive line alongside
Alexei Kovalev and
Tomáš Plekanec. He amassed 53 points in 78 games and was joined by his younger brother Sergei, who had been called up from Hamilton, midway through the season. Entering the playoffs with the Canadiens as the first seed, Andrei and Sergei both scored in their NHL postseason debuts against the
Boston Bruins less than two minutes apart. They also both finished with eight points each in 12 playoff games. However, the Canadiens were defeated by the
Philadelphia Flyers in the Eastern Conference Semifinals. On 1 July 2008, he signed a three-year extension worth an annual salary of $3.25 million with the Canadiens. Several games into the
2008–09 season, he suffered a
concussion when he was checked into the boards by
Kurt Sauer of the
Phoenix Coyotes. Kostitsyn laid on the ice for several minutes before needing to be helped off the ice. He returned to the team after missing two games. In December 2008, he missed another two games due to a minor leg injury, then returned to notch his first career NHL
hat-trick on 27 December, in a 3–2 win over the
Pittsburgh Penguins.
Nashville Predators On 27 February 2012, Kostitsyn was traded to the
Nashville Predators for a second-round pick in 2013 and a fifth-round pick in 2013. On 1 May 2012, Kostitsyn and Predators' teammate
Alexander Radulov were spotted at a
Scottsdale bar at 5:00 a.m. the night before Game 2 of their second-round
playoff series against the Coyotes, thus breaking curfew. Both were subsequently suspended by the Predators' management for Game 3. Said Predators' general manager
David Poile of the incident: "What they did was unacceptable and the coaches and myself had to come to the plate and do the right thing for the team. It happened. It's really unfortunate. It's selfish behavior and we'll just have to leave it at that."
Return to Russia During the 2012 off-season, the Predators made it evident that they would not bring back Kostitsyn, although the Predators later re-signed his brother, Sergei. On 14 September 2012, Kostitsyn returned to Russia and signed a one-year contract with
Traktor Chelyabinsk of the
Kontinental Hockey League (KHL). In the
2014–15 season, his third with Traktor, Kostitsyn was traded to the expansion club,
Sochi on 29 October 2014. On 1 June 2017, Kostitsyn continued his career in the KHL, signing a one-year deal with Chinese outfit,
Kunlun Red Star. After a further two seasons in his native Belarus with Dinamo Minsk, on 6 May 2020, Kostitsyn signed a one-year deal to continue in the KHL, with Russian team,
HC Neftekhimik Nizhnekamsk. ==International play==