The Marlins announced that Nunez will return to his home in the Dominican Republic to deal with a personal matter.
When the veteran reliever will be eligible to return to the big leagues remains unclear, as he reportedly is dealing with an issue of identity.
According to The Associated Press, Nunez has been playing under an assumed name. The AP story said the Marlins have been aware for several months, and that Nunez's real name is Juan Carlos Oviedo.
Nunez's age also is in question. The Marlins list him at age 28, while the AP reports the reliever is 29.
Nunez pitched for the Marlins on Wednesday night, tossing a scoreless ninth inning in a non-save situation in a 4-0 win over the Braves at Sun Life Stadium.
On Thursday, the Marlins were off and traveled to Milwaukee, where they will face the Brewers in a three-game series beginning on Friday. Due to his personal matter, Nunez remained in South Florida as he made plans to return to his home in the Dominican Republic.
The reliever is making $3.65 million this year, but he is not being paid for the final six games.
The Marlins have been internally discussing whether to bring back Nunez, who has a 4.06 ERA and is tied for seventh in the National League with 36 saves in 68 games. If the reported identity issue lingers, it possibly could impact his status for 2012.
With Nunez gone for the final six games, Edward Mujica and Clay Hensley are options to be used at closer.