It said the Veterinary Medical Center expects to maintain voluntary isolation for an additional seven days as clinicians investigate the case.
As of Monday, no new cases had been reported.
The index case was in a horse admitted last Thursday. The university said the animal was euthanised within hours of admission.
The university said that due to the potential for spread of EHV-1 among horses and camelids, movement to and from the equine hospital is restricted.
"It is important to note there is not currently an active case of EHV-1 in the hospital, and we are taking every precaution to prevent the spread of disease."
The hospital said the horse was down when it arrived at the hospital at 2pm on Thursday.
The horse was kept in a separate area of the equine hospital. Within hours, the horse's condition deteriorated, and the animal was euthanized.
EHV is a common virus found in horse populations around the world. Almost all horses older than two years of age have been exposed to it.
While many horses can carry the virus with no or minimal signs of illness, it occasionally causes some to develop serious clinical signs; therefore, the hospital said it was "exercising an abundance of precaution".
It is unknown what causes some horses to develop the serious neurological form, however most cases are associated with a mutated form of the virus.
EHV-1 can manifest itself in four ways: neurological form, respiratory disease, abortion, and neonatal death. The neurological form is called Equine Herpesvirus Myeloencephalopathy (EHM). It is not contagious to people.