Surgery is a possibility, general manager Kim Ng said.
"The most important thing for us right now is to give it some time to let the inflammation, pain and discomfort subside before we can give any further evaluation," Ng said.
The Marlins reinstated Isan Diaz from the injured list. In Anderson's absence, Diaz and Jon Berti are expected to share time at third.
Anderson is batting .250 with three homers and 11 RBIs.