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. Babchuk was the only possible defenceman they could send down because he was the only one on the Hurricanes' roster that was not subject to waiver wire claims. The next day, Carolina announced that they had suspended Babchuk because of his refusal to report to Albany. In 2007–08, Babchuk played in the Russian Superleague (RSL) for Avangard Omsk.