Cabrera, last year's first Triple Crown winner since 1967 and reigning American League MVP, led the first AL balloting of the season with 1,500,165 votes.
Along with Cabrera, New York Yankees second baseman Robinson Cano (1,235,230 votes) and Los Angeles Angels outfielder Mike Trout make up the top three overall AL vote-getters.
Baltimore Orioles rookie Manny Machado, 20, is second in the balloting at third base with 723,943 votes.
Cabrera, a seven-time All-Star who has never been elected a starter, leads the major leagues with a .367 batting average, 83 hits and 65 RBI.
Other leading vote-getters by position include: Orioles first baseman Chris Davis (1,176,016 votes), Texas Rangers shortstop Elvis Andrus (727,555), Orioles center fielder Adam Jones (1,181,875), Tigers right fielder Torii Hunter and Minnesota Twins catcher Joe Mauer (863,450).
The All-Star Game is July 16 at Citi Field in New York.
The first National League balloting results will be announced Tuesday.
When the in-stadium phase of balloting concludes June 28, fans can vote exclusively online at MLB.com until July 4 at 11:59 p.m. ET. All-Star teams will be announced July 7 on TBS.
Fans can also vote among 10 AL and 10 NL candidates for the July 15 Home Run Derby. The AL candidates are: Jose Bautista (Toronto Blue Jays), Adrian Beltre (Rangers), Cabrera, Cano, Adam Dunn (Chicago White Sox), Prince Fielder (Tigers), Josh Hamilton (Angels), Jones, Evan Longoria (Tampa Bay Rays) and Mike Trout.
The NL candidates are: Carlos Beltran (St. Louis Cardinals), Ryan Braun (Milwaukee Brewers), Bryce Harper (Washington Nationals), Jason Heyward (Atlanta Braves), Matt Kemp (Los Angeles Dodgers), Andrew McCutchen (Pittsburgh Pirates), Buster Posey (San Francisco Giants), Giancarlo Stanton (Miami Marlins), Joey Votto (Cincinnati Reds) and David Wright (New York Mets).
Additionally, fans will be able to vote for one player from a list of five from each league over a four-day period with the winners announced after the voting concludes on July 11.