Four horses died following the discovery of the equine herpes virus (EHV-1) at the Crofton Manor Equestrian Centre near Fareham.
The strain, which can cause inflammation of blood vessels in the spinal cord and brain, is spread by direct horse-to-horse contact.
It can also be spread indirectly through contact with physical objects that are contaminated with the virus, such as clothing, feed and water buckets and grooming equipment.
Clerk to the verderers Sue Westwood told the A&T: “The verderers are, of course, aware of the cases of EHV-1 at Crofton Manor Equestrian Centre.
“The verderers are asking anyone whose horse has been to Crofton Manor, or has had contact with a horse that has been to Crofton Manor since Christmas, to kindly refrain from riding on the Forest.”
She added: “This is a temporary measure to protect the Forest ponies. If you have any concerns regarding EHV-1, please contact your vet for advice. The situation may well change and we will update as and when we learn more and if our advice needs to be altered.”
Alan Hough, of the Celtic Equine Veterinary Practice in Minstead, told the A&T: “Our deepest sympathies go out to the owners of the four horses that have died in the current EHV outbreak.
“There are five different types of equine herpes virus which infect the domestic horse – there are two types in particular which commonly cause clinical symptoms. These are EHV-1 and EHV-4. These two types of EHV are responsible for flu-like respiratory disease, neurological disease and abortion in pregnant mares. The virus is airborne and can spread very easily.
“Your horse is at greater risk of contracting EHV if they are at a breeding stud or live at a yard with pregnant mares, or are at a livery yard where horses are frequently being moved, and at competition venues.”
Mr Hough said at-risk animals should be placed in isolation for 14 days and undergo daily clinical monitoring. Those which develop symptoms such as fever and nasal discharge should undergo veterinary examination.
Horses can also be vaccinated against EHV-1, but this is not advisable if the animal could be harbouring the virus already.