Martinez isn't the only Yankees player to lead at his position. Alex Rodriguez remains the leader at third base, holding off Boston's Bill Mueller and Baltimore's Melvin Mora.
Fans can vote up to 25 times through the Ameriquest 2005 All-Star Online Ballot available at MLB.com and Yankees.com. Online voting ends at 11:59 p.m. ET on June 30. Voting at Yankee Stadium ends on June 24, with the teams being announced on July 3.
Martinez has led at first base since voting began, but Teixeira has cut significantly into his lead. Martinez, who led the AL with 10 home runs in May while homering in seven of eight starts at one point, has cooled off considerably in June.
Behind the two first basemen are Boston's Kevin Millar, Chicago's Paul Konerko and Seattle's Richie Sexson.
Derek Jeter, who started last year's Midsummer Classic, remains a close second to Baltimore's Miguel Tejada at shortstop, with Boston's Edgar Renteria, Detroit's Carlos Guillen and Texas' Michael Young rounding out the top five.
Gary Sheffield (fifth) and Hideki Matsui (sixth) stand pat once again this week in the outfield vote. Boston's Manny Ramirez, Seattle's Ichiro Suzuki and Anaheim's Vladimir Guerrero continue to man the top three spots, while Boston's Johnny Damon is fourth.
Jorge Posada trails Boston's Jason Varitek and Detroit's Ivan Rodriguez at catcher, while Jason Giambi remains third in the DH vote behind Boston's David Ortiz and Baltimore's Rafael Palmeiro.
Tony Womack remains fourth in the second-base race, with Baltimore's Brian Roberts, Texas' Alfonso Soriano and Boston's Mark Bellhorn all ahead of him.
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.