Kemp joins Raul Mondesi, who accomplished the feat in 1997 and '99. He did so on a 3-1 pitch off lefty reliever Matt Reynolds.
As Dodger Stadium fans chanted "MVP," Kemp took three pitches and fouled one off before he crushed the fastball 427 feet to straightaway center field.
"I've always thought I could do it," Kemp said. "I can run. I can put a little bit of power in it. I just had to put it all together at the same time. It's pretty special."
On the season, Kemp is hitting .323 with 98 RBIs to go along with his 30 homers and 33 steals. He is in the top four in the league in all three categories.
"I'm just happy I got to do it here in L.A.," Kemp said after the game. "The fans have always supported me. We still got a long way to go."
No Dodger has ever reached the 40-40 club, and when Kemp was asked about the mark, he responded, "Maybe one day."
Manager Don Mattingly praised Kemp both before and after the game, specifically noting how much Kemp's leadership role has meant to the team.
"It's been a tremendous season for him in all areas of his game -- leadership and the whole thing," Mattingly said. "It's been a joy really to have Matt playing this way, and his leadership in the dugout. The presence he brings, but not only that, this guy gets ready to play every day and plays hard every day."
The last Major Leaguer to reach the 30-30 club was Texas second baseman Ian Kinsler, in 2009.
AJ Cassavell is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.