Babenko was drafted by the Colorado Avalanche in 1996 in the 2nd round, 51st overall. After a season in the Ontario Hockey League for the Plymouth Whalers, Babenko joined the Avalanche organization in 1998. After three seasons in the American Hockey League for the Hershey Bears, he finally made his NHL debut for Colorado during the 2000–01 NHL season, playing 3 games in all without registering a point.