A creative, feisty forward, Grabovski was selected by the Montreal Canadiens in the fifth round (No. 150) in the 2004 NHL Draft.

The German-born Grabovski remained in Russia, where he was playing for Neftekhimik. He joined Dynamo Moscow in 2005-06 before signing with Montreal and heading to North America to start the 2006-07 season.

The 5-foot-11, 186-pound Grabovski spent most of that season with Hamilton of the American Hockey League, scoring 17 goals and 54 points in 66 games. He played three games for the Canadiens and made his NHL debut on Jan. 6, 2007, against the New York Rangers. During the AHL postseason, Grabovski had four goals and 11 points to help Hamilton win the Calder Cup.

Grabovski started the following season with the Canadiens and scored his first NHL goal on Oct. 22, 2007, against Manny Fernandez of the Boston Bruins. He played 24 games with Montreal and 12 for Hamilton that season.

On July 3, 2008, Grabovski was traded to the Toronto Maple Leafs for Greg Pateryn and a 2010 second-round draft pick. In his first season with the Maple Leafs, he had 20 goals and 48 points, ranking third among NHL rookies in each category. Following the lockout-shortened 48-game season in 2012-13, when he had nine goals and 16 points, Toronto bought out the remaining four years of his contract, making Grabovski a free agent.

Grabovski signed a one-year contract with the Washington Capitals on Aug. 23, 2013. On opening night of the 2013-14 season, he had a hat trick and four points against the Chicago Blackhawks.

After one season with Washington, Grabovski signed a four-year contract with the New York Islanders on July 2, 2014.