Kershaw led all Major League starters in innings, strikeouts, ERA and WHIP (0.52) on the month.
Kershaw threw three shutouts in May, blanking the Padres on May 1, the Mets on May 12 and the Reds on May 23. He posted double-digit strikeouts in all but one start, fanning a season-high 14 on May 1 against San Diego.
He is now 7-1 with a 1.56 ERA, 105 strikeouts and five walks in 11 starts this season.
This is Kershaw's sixth career monthly honor.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth.