Kershaw, 23, tied the National League lead in victories with his 21-5 record and had a 2.28 ERA with 248 strikeouts. He becomes the eighth Dodger pitcher to win the award -- Sandy Koufax won it three times -- and the youngest player since the New York Mets Dwight Gooden won in 1985 at age 20, MLB.com said.
Kershaw received 27 of a possible 32 first-place votes, and a total 207 votes, in balloting by the Baseball Writers' Association of America. Phillies pitcher Roy Halladay was second with 133 votes and Philadelphia teammate Cliff Lee third with 90 votes. Halladay had four first-place votes.
Other Dodgers to win the Cy Young Award were Don Newcombe in 1956, Don Drysdale in 1962, Koufax in 1964, 1965 and 1966, Mike Marshall in 1974, Fernando Valenzuela in his 1981 rookie season, Orel Hershiser in 1988 and Greg Gagne in 2003.
Kershaw joined the Dodgers as the seventh overall selection in the 2006 draft and was named Opening Day pitcher in his third season. He won a Gold Glove earlier this month and the Warren Spahn Award as the best lefty in the major leagues.