Kershaw could still make the team. Puig, who sat out six weeks because of injury, will not.
Pitcher Zack Greinke, first baseman Adrian Gonzalez, catcher Yasmani Grandal and center fielder Joc Pederson all were selected to the team. The Dodgers quartet will be joined at the All-Star game by the Angels' dynamic duo of Mike Trout and Albert Pujols.
Pujols was selected Monday as a reserve first baseman, then named to start for the American League in place of the injured Miguel Cabrera.
Greinke, who is 7-2 and leads the major leagues with a 1.48 earned-run average, is one of the candidates to start as the NL pitcher. The other candidates to start include Max Scherzer of the Washington Nationals (9-6, 1.82), Gerrit Cole of the Pittsburgh Pirates (12-3, 2.28), and Madison Bumgarner of the San Francisco Giants (8-5, 3.34).
Kershaw, the Dodgers' ace, threw his support behind Greinke.
"I'm sure it's probably between him and Scherzer. You can't go wrong either way," Kershaw said, "but I'm a little biased, probably."
The starting pitcher will be selected by Bumgarner's manager, Bruce Bochy, who earned the right to manage the NL squad because the Giants were NL champions last season.
Bochy bypassed Kershaw two years ago, when the All-Star game was played in New York, in favor of Matt Harvey, then the rookie sensation of the New York Mets. Bochy also bypassed Kershaw on Monday, using his picks on Bumgarner, A.J. Burnett of the Pirates and Michael Wacha of the St. Louis Cardinals.
"I'm fine with Boch. He's great," Kershaw said. "If Donnie [Mattingly] was the manager and it was the same situation, I would hope I would get to go."
Kershaw is 5-6 with a 3.08 ERA, but he leads the major leagues in strikeouts, and several advanced metrics rate him and Scherzer as the top two starting pitchers in the NL.
Kershaw was selected as one of five players for the "Final Vote," and he could make the All-Star team for the fifth consecutive season. If Kershaw is elected in fan voting this week, the Dodgers would have five All-Stars for the first time since 1995, when Mike Piazza, Hideo Nomo, Raul Mondesi, Jose Offerman and Todd Worrell represented the team.
Greinke made the All-Star team for the second consecutive season and third time overall. Gonzalez, who made an All-Star team for the fifth time in his career and his first time with the Dodgers, hit his 16th home run Monday night and was batting .291 before the game against Philadelphia.
The selections further validated the Dodgers' then-maligned winter trade of Matt Kemp to the San Diego Padres, in which the Dodgers got Grandal and cleared an outfield spot for Pederson.
Grandal was batting .277 before Monday, when he hit his 13th home run, tops among NL catchers His .890 OPS also led all NL players at his position. He said he already had tickets to spend the All-Star break in Las Vegas but would happily change plans to play in the game.
"I'm humbled," Grandal said.
Pederson began Monday batting .234 with 20 home runs, tied for fifth in the league. He is the first rookie to represent the Dodgers in the All-Star game since Nomo in 1995.
"I think that's the only reason I was picked for the All-Star team — because I have some homers," Pederson said.
Pujols leads the AL with 25 home runs. He is in the fourth season of a 10-year, $240-million contract with the Angels. This will be his first All-Star appearance with the Angels, after making nine appearances in his 11 seasons with the St. Louis Cardinals.
The Kansas City Royals could have seven players on the AL team. Fans elected four players — catcher Salvador Perez, shortstop Alcides Escobar and outfielders Lorenzo Cain and Alex Gordon — and pitchers Wade Davis and Kelvin Herrera were selected Monday. Third baseman Mike Moustakas is one of the AL "Final Vote" contestants.
The players also vote, with their ballots used to help determine reserves and starters. Major League Baseball releases the player ballot totals, and AL players did not vote for a Kansas City player to start at any position.