In all, about 80 horses were living on the property at the centre of the infection.
There is no evidence to date that the infection had spread beyond the index herd, but several horses on a nearby property were being tested. None had tested positive to the disease to date.
Swamp fever is caused by a virus that is usually transmitted by the transfer of blood from infected horses to susceptible ones by large blood-feeding insects or by the shared used of blood-contaminated instruments or needles.
Cases can be acute, chronic or not apparent at all.
The virus attacks the immune system, with symtpoms including bleeding in mucus membranes and a gradual loss of condition and muscle weakness. Other signs include fever, depression and anaemia.
Infected horses continue to carry the virus and can be the source of further infections, hence the decision to euthanise the animals.
The Arkansas state veterinarian, Dr Pat Badley, said the infection seems to be isolated to the single herd.
"The owner of the herd does not show horses nor do they sell any horses to any extent," he said.
"The index herd has only one adjacent herd," he added.
The source of the infection has not been found, Badley said.
"The most recent addition to the index herd was traced back to its origin. Those horses had all negative EIA tests but were retested by Arkansas Livestock Poultry Commission personnel and all their horses were negative," he said.
Badley described the number of positives horses in the index herd as substantial and alarming.
He said the commission was investigating all leads to ensure the outbreak did not spread from the index herd.
"Since the index herd has added horses over the years some of those horses may have been the source of infection," Badley said.
The herd had been quarantined from the time of the first positive test, he said, and added that there had not been any information to date that warranted cancelling horse shows.
The first positive test on the property was about three weeks ago.