Ramirez was fourth among the outfielders in the first round of balloting for the National League, which was released Tuesday.
Online voting started April 22, two weeks before Ramirez was handed a 50-game ban. Fans can vote online at mlb.com until July 2.
Balloting at stadiums ends June 28. The All-Star game will be played July 14 in St. Louis.
Team spokesman Josh Rawitch said there are no plans for the Dodgers to campaign on behalf of Ramirez or any other player.
Ramirez is the only Dodger with a legitimate shot at starting in the All-Star game.
Orlando Hudson (314,103) is third among second basemen, but has less than half as many votes as Chase Utley of Philadelphia (675,596).
Martin (261,917) is fourth among catchers, but is nearly 200,000 votes behind Yadier Molina of St. Louis (451,368).
More on Ramirez
With the Dodgers on the road for the rest of the week, Ramirez is expected to continue his mid-morning workouts at Dodger Stadium.
Ramirez practiced Tuesday for only the second time since his May 7 suspension.
He is lifting weights, doing agility drills, hitting against live pitching and doing some throwing, though most of the work takes place out of public view under the grandstands.
Ramirez can work out with the team when the Dodgers return home June 1 but that isn't likely to happen. Instead, Ramirez will probably continue his workouts at the team's spring-training facility in Arizona.
Mota back on track?
Guillermo Mota tossed a scoreless ninth inning Monday, extending his streak of shutout innings to three.
That might not seem like much, but it's significant to Mota, who had an earned-run average of 9.00 only four days ago and looked to be a waste of the $2.35 million the Dodgers agreed to pay him last winter.
"My confidence never left me," he said. "It never felt like it was something insurmountable."
Mota, 35, said that pitching coach Rick Honeycutt found the key to turning around his season when viewing tape of him pitching for the Dodgers in 2003 and 2004.
Honeycutt told Mota that his leg kick was too upright and told him to go back to doing what he used to do, which was to swing his leg back.
The Dodgers continued to be cautious with Rafael Furcal, who has experienced pain in his buttocks, and held him out of the lineup for the second consecutive day. Furcal said he wanted to play Tuesday and that he expects to play today.
Hiroki Kuroda will make his second rehabilitation start with Class-A Inland Empire tonight.
Jason Schmidt had to halt his latest rehabilitation assignment because of irritation in his surgically repaired shoulder. . . . Andre Ethier (toe) was back in the lineup.
Baxter contributed to this report from Los Angeles.