[1] He began his training with the Sokil Kyiv junior hockey affiliate, a team which included fellow future Ukrainian NHLer Nikolai Zherdev.

The rival team's coach, Ravil Iskakhov, took note of both Babchuk and Zherdev, and invited the pair to further their development with the Elemash Elektrostal hockey club of the Russian Major League, to which they accepted together.

In the 2006–07 season, on February 6, 2007, the Hurricanes activated František Kaberle from injury, forcing them to send Babchuk down to the Albany River Rats.

Following a contract dispute that lead to him requesting a trade out of Carolina, Babchuk turned back to Russia on 19 September 2009, re-signing with Kontinental Hockey League (KHL) club Avangard Omsk.

[8][9] Babchuk was chosen to play on Team Yashin at the 2nd Kontinental Hockey League All-Star Game.

On November 17, 2010, Babchuk was traded along with Tom Kostopoulos to the Calgary Flames for Ian White and Brett Sutter.