"He's not going to do anything on the field today," said Melvin, "and then we'll see how he is on the field come tomorrow."
If Cespedes is able to play Wednesday, it will be in the designated-hitter role.
Craig Gentry made the start in left field and went 1-for-3 in Tuesday's 3-0 loss in place of Cespedes, who is riding a career-high 14-game hitting streak with a .351 average during that span.
The Cuban slugger hit .324 in 26 games in June after batting just .245 over his first 52 games. Those numbers, combined with a spike in outfield assists -- most of them highlight-worthy -- have led to a large boost in All-Star support.
Cespedes currently ranks third among all American League outfielders. Fans can cast their votes for starters at MLB.com -- online or on a mobile device -- using the 2014 All-Star Game MLB.com Ballot Sponsored by Experian until Thursday at 8:59 p.m. CT. The 2014 All-Star Game will be played at Target Field on Tuesday, July 15 on FOX.
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.