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.

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.

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.

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.

[10] On 1 June 2017, Kostitsyn continued his career in the KHL, signing a one-year deal with Chinese outfit, Kunlun Red Star.

[11] 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.

Kostitsyn made his second under-20 appearance at the 2002 World Junior Ice Hockey Championships and scored three goals to help Belarus stay in the top division.

Later that year, Kostitsyn returned to the top division at the 2002 IIHF World U18 Championships, recording 10 points in eight games and helping lead Belarus to a fifth-place finish.

Competing in his third under-20 tournament at the 2003 World Junior Ice Hockey Championships, Kostitsyn recorded two goals and one assist, but was relegated with Belarus to Division-I for 2004.

On 23 December 2009, Kostitsyn was selected along with his younger brother Sergei, Mikhail Grabovski and Ruslan Salei as the only four current NHL players to represent Belarus in the 2010 Olympics.