The agency said the employees were driving in a remote area on the morning of Sept. 20 when a bullet hit their unmarked vehicle.
No one was hurt, but Blue Mesa Loop Road and all trails leading into the Blue Mesa area were closed due to the investigation.
Williams was booked into jail and is accused of aggravated assault and endangerment.
Matthew Williams, a 21-year-old resident of Chambers, Arizona, is accused of shooting at two National Park Service employees in the Petrified Forest National Park. (Apache County Sheriff's Office)