Stefanovich's career started out in his home country of Belarus, spending just over two seasons in Belarus' tier two hockey league – half a season with HC Dinamo-2 Minsk, and just over one and a half seasons with HC Homiel-2. After playing just three games with HC Homiel-2 in the 2006–07 tier two season, HC Homiel of the Belarusian Extraliga called him up. He finished the rest of the season with Homiel and drew a great deal of attention from North American teams. Following the season with Homiel, Stefanovich was selected 54th overall in the 2007 CHL Import Draft by the Quebec Remparts. Upon arriving in Canada, Stefanovich made the Remparts roster and quickly adjusted to the North American-style of hockey. Halfway through his inaugural QMJHL season, Stefanovich was selected to play in the CHL Top Prospects Game and, following the conclusion of the season, received the Mike Bossy Trophy, which is awarded to the QMJHL player judged to be the best professional prospect. Scouts have identified that Stefanovich possesses a quick and accurate wrist shot and superb offensive instincts, but is not an overtly physical player, even for someone of his large stature. It is also said that his play is inconsistent and his skating is sub-par, but that he has above-average hockey sense and play-reading ability. Stefanovich's play in the 2008–09 QMJHL season improved and he became a more consistent player. These improvements have been credited, some say, to his pre-season tryout with the Maple Leafs, where he befriended fellow Belarusian Mikhail Grabovski and RussianNikolai Kulemin. In order to make the team, he realized he needed to improve these negative aspects of his game. On 1 June 2009, Stefanovich was selected second overall in the 2009 KHL Junior Draft by HC Dinamo Minsk. Two days later, on 3 June, he was signed to an entry-level contract by the Maple Leafs. On 19 September 2009, Stefanovich was assigned to the Toronto Marlies, the AHL affiliate of the Maple Leafs, and shortly after demoted back to junior. On 15 September 2010, the Maple Leafs announced that Stefanovich would be part of the team's 63-player training camp roster, however, eight days later, the team assigned him to the Toronto Marlies. Stefanovich was named to the Marlies' opening day roster on 8 October, but was reassigned to the Reading Royals on 14 October 2010. On 18 October, Stefanovich was recalled to the Marlies. After playing only 2 games with the Marlies, he was again reassigned to the Royals on 22 November 2010. Stefanovich was loaned out to HC Dinamo Minsk of the KHL on 27 November 2010. On 13 January 2011, Stefanovich's NHL rights were traded by the Maple Leafs to the Dallas Stars for Fabian Brunnstrom. During his second season in the Russian second tier league, the VHL, with Dizel Penza, Stefanovich was provisionally suspended on 20 November for failing an anti-doping test. He played no further part in the season with Dizel and on 27 April 2015, was given a two-year ban backdated to 10 November, for the doping violation. On 26 August 2015, he returned to North American and signed a one-year ECHL contract with the Rapid City Rush.
