The 28-year-old mare was found dead by a hunter on Saturday and reported to park rangers the following day.
Trish Kicklighter, superintendent of Assateague Island National Seashore, said she's saddened by the incident and hopes the shooting was accidental.
Chief Ranger Ted Morlock said rangers are pursuing several good leads. He said failure to report the shooting violates park service regulations.
There are more than 300 wild ponies on Assateague, a barrier island that straddles the Maryland-Virginia line. Every summer on the Virginia side of the island, the ponies are rounded up and swim
across the Assateague Channel to Chincoteague, where foals are auctioned off.