Grabovski was drafted by the Montreal Canadiens in the 2004 NHL Entry Draft, 150th overall. He played his first NHL game on January 6, 2007 against the New York Rangers. Grabovski played three games in the NHL before being sent back down to Montreal's AHL affiliate, the Hamilton Bulldogs. He failed to record a point in any of those games, but impressed fans with his speed and his agility.
Grabovski started the 2007–2008 season with the Canadiens, recording his first NHL point in an October 20, 2007 game against the Buffalo Sabres, and his first goal two days later against the Boston Bruins. After a March 6, 2008 game in Phoenix for which he was a healthy scratch, Grabovski, apparently frustrated by his exclusion from the lineup, flew to Los Angeles ahead of the rest of the team to speak with his agent. Such a deliberate move to separate himself from his teammates created controversy in Montreal.
Grabovski was traded to the Maple Leafs on July 3, 2008 in exchange for the draft rights to Greg Pateryn and a 2010 second round pick. He has since become a valuable player to their team, being their first player to score 10 goals and being among the top NHL rookies in goal scoring throughout the 2008-09 season. Grabovski has formed a potent scoring line with Niklas Hagman and Nikolai Kulemin. Each of the three players are playing in their first season with the Maple Leafs, and have proved to be a credible source of speed and skill for the young Maple Leafs team. During a game against his former team, the Canadiens, Grabovski was the subject of constant physical attention from the Canadiens, including a hit away from the play from captain Saku Koivu, and a charge from Sergei Kostitsyn. The latter resulted in a game misconduct penalty and Kostitsyn's ejection from the game.
Grabovski has represented his adopted home country of Belarus in international play as well. He scored 4 goals in one game against tournament hosts Austria in the 2005 Men's World Ice Hockey Championships.