Marlins manager Dan Jennings said they will have the results of the additional tests later in the week.
"I hope for his sake and ultimately our sake that they can determine the cause of that and find some resolution," Jennings said. "We need him back."
Cosart hasn't pitched in the Majors since July 4, as he was optioned to Triple-A New Orleans the following day. He has struggled for the Marlins this season, going 1-4 with a 5.36 ERA in nine games.
Jake Rill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.