A New Forest pony died after being hit by a silver/grey camper van at Pound Lane, Burley, at 2.30pm on February 26.
The female driver spoke to a witness before driving off without leaving their details.
Posting on social media New Forest Roads Awareness said the injured pony “staggered off” but died a short distance away.
The group added: “She has not, as far as we are aware, reported the incident to police.”
Members urged anyone with information about a damaged camper van to contact the police or the New Forest Verderers.
The Verderers offer a reward of up to £5,000 for information leading to the conviction of a hit-and-run driver.
A Verderers’ spokesperson confirmed that the Burley collision had been logged as a hit-and-run.