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 Under-18 Championships and silver medals with the junior team at the 2005 and 2006IIHF 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. Khudobin then played as a backup for Metallurg before deciding to move to North America and play in the Canadian major junior hockey system. He opted to join the Saskatoon Blades of the Western Hockey League for the 2005–06 season, helping them to their best regular season finish in over a decade and backstopped them past the first round of the playoffs for the first time in six years. In 2006, Khudobin returned to Russia and took over back-up goaltending duties for Metallurg in the Russian Superleague, helping the team to the league championship. In the summer of 2007, however, three years after initially being drafted, Khudobin signed a three-year, entry-level contract with the Wild.
Minnesota Wild
Khudobin spent the following season splitting time between the American Hockey League 's Houston Aeros and the ECHL's Texas Wildcatters, earning top ECHL goaltender honors for 2007–08. In 2009–10, he made the full-time jump to the Aeros and later made his NHL debut for the Wild on 4 February 2010, replacing the injured Josh Harding in a 4–2 win over the Edmonton Oilers. He made his first NHL start two days later on 6 February 2010, stopping 38 of 39 shots in a 2–1 win over the Philadelphia Flyers. Following a 24 September 2010, pre-season knee injury to Harding, the Wild's full-time back-up goaltender, Khudobin was expected to take over that role for the Wild. However, the Wild instead signed José Théodore to a one-year contract, leaving Khudobin in the number-three position. Soon after the signing Khudobin was returned to Houston. Khudobin was recalled by the Wild on 8 January 2011 to back-up Théodore after starter Niklas Bäckström suffered a strained hip flexor. On 12 January, Théodore suffered a similar injury, and Khudobin replaced him in the third period of a 5–1 loss to the Nashville Predators. After a 4–1 loss to the visiting Colorado Avalanche on 14 January, Khudobin posted his first career NHL shutout, making 32 saves in a 4–0 win over the visiting Vancouver Canucks.
Boston Bruins
Nearing the 2011 NHL trade deadline, Khudobin was traded to the Boston Bruins on 28 February 2011 in exchange for Jeff Penner and Mikko Lehtonen. Khudobin was then assigned to the AHL's Providence Bruins. He finished the season strong and was called up as an emergency goalie for Boston during their 2011 Stanley Cup playoff run; he was included in the team's celebratory picture after Boston won in the Finals and was also awarded a Stanley Cup ring for his inclusion in the squad. However, due to the fact that he did not play for Boston during the 2010–11 season, his name was not engraved on the Stanley Cup. On 1 July 2011, Khudobin signed a new two-year contract with the Bruins. On 5 April 2012, he played his first game with the Bruins, earning a win against the Ottawa Senators. He later served as backup to Tuukka Rask during the lockout-shortened 2012–13 season.
Carolina Hurricanes
On 5 July 2013, the Carolina Hurricanes signed Khudobin as a free agent to one-year, one-way contract paying $800,000. Following the 2013–14 season, he signed a new two-year, $4.5 million contract with Carolina.
As a free agent at the conclusion of the 2015–16 season with the Ducks, on 1 July 2016, Khudobin signed a two-year contract to return to the Boston Bruins.
Dallas Stars
On 1 July 2018, Khudobin joined his fifth NHL club as a free agent, agreeing to a two-year, $5 million contract to assume backup duties for the Dallas Stars.
