"It's hard to imagine why she was attacked so viciously," Wildlife Rehab of Greenville wrote on its Facebook page.
The organization reported the incident to the South Carolina Department of Natural Resources, the television station reported.
SCDNR spokesman David Lucas told WSAV his organization received a number of other calls this week about the opossum and Wildlife Rehab of Greenville's Facebook post.
Luca said it was unclear which golf course the opossum was attacked at, the television station reported. However, Watson said Wildlife Rehab of Greenville would release that information to the SCDNR; she did not reveal the name of the course.
"This event should not reflect on the golf course or the city of Hilton Head," Watson told WJCL. "This act is the sole responsibility of the sick person or persons who attacked this baby.
The rehab center has received more than $6,000 in donations to care for Scarlett, WYFF reported.