Infante learned on Sunday morning that his grandfather had passed away. The veteran has been excused by the team to travel back to his native country, Venezuela, for the funeral.
Initially, Infante was in the lineup, batting second on Sunday in the series finale against the Indians at Progressive Field. But shortly after arriving at the ballpark, Infante informed the organization.
Donnie Murphy was given the start at second base in Infante's place.
"[Infante's] grandfather passed away this morning," manager Ozzie Guillen said. "I expect him to be back in three days, I guess. I don't know."
Infante has been the team's most consistent hitter, batting .326 with six home runs and 20 RBIs.
"We're going to keep in touch in the next couple of hours," Guillen said. "It's a tough situation. That happened to me a few years ago."
After completing their series at Cleveland on Sunday, the Marlins will return to Marlins Park to face the Rockies next week. Perhaps Wednesday will be the day Infante is back.
Along with Murphy, Donovan Solano is a candidate to play second base.
Solano was called up on Sunday from Triple-A New Orleans, marking his first appearance on a big league roster.
"Murphy is going to play today, and we'll see what happens in the next couple of days," Guillen said of filling in at second.
As a team, the Marlins are now without Infante and center fielder Emilio Bonifacio, who was placed on the 15-day disabled list on Sunday with a sprained left thumb.
"We have to overcome," Guillen said. "We've got to be tough."