Marlins manager Mike Redmond, who called the injury a bruised elbow, said Hechavarria had no ligament damage.
"It's not a ligament thing, which is great," Redmond said. "It'll just be a matter of taking a break and getting some rest. Hopefully it's a short-term thing."
Redmond believes Hechavarria will be ready to throw in the next week or so.
Injuries keep sidetracking a young club looking to establish continuity. As All-Star outfielder Giancarlo Stanton returns after missing six games with a bruised shoulder, Hechavarria is headed to the DL.
In 14 games, Hechavarria, who turned 24 on Monday, is batting .184, but he has been solid defensively.
The Marlins acquired the Cuban-born shortstop from the Blue Jays last November, and he is one of the core pieces of a rebuilt roster.
Replacing Hechavarria on the active roster is veteran Nick Green, who had his contract selected from Triple-A New Orleans.
Because their 40-man roster was already at its maximum, Miami created space for Green by transferring right-hander Nathan Eovaldi to the 60-day disabled list.
Eovaldi, initially projected to be the No. 2 starter, opened the season on the 15-day DL with right shoulder inflammation. Moving Eovaldi to the 60-day disabled list is a blow to the rotation. He now won't be eligible to be activated until the middle of June, at the earliest.
In their last six games, the Marlins have had to scratch four different players due to injuries.
The Marlins opened a four-game series at Cincinnati on Thursday.
Off to a 3-12 start, the Marlins have already had to use 14 different lineups in 15 games. That will change to 15 in 16 games on Thursday night.
"I'd like to be adding guys -- not adding and subtracting them," Redmond said. "There's not much you can do. We've had a bunch of guys get banged up. We just keep going, keep moving."