Born to a Kazakh father of Russian descent, Valeri, and a Russian mother, Tatiana, Khudobin began his hockey career in his native Kazakhstan but moved to Russia at age 13 and joined the Metallurg hockey school in Magnitogorsk in order to develop his game at a higher level. He was a consistent starter for Russia's national junior squads, earning a gold medal with the under-18 team at the 2004 IIHF World U18 Championships and silver medals with the junior team at the 2005 and 2006 IIHF World Junior Ice Hockey Championships. At the end of this 2003–04 hockey season, Khudobin was drafted by the Minnesota Wild at the 2004 NHL Entry Draft in the seventh round, 206th overall.