The virus was found in the Heath Isolation Unit, in a maiden filly which had arrived from overseas on 20 January and has been fully vaccinated.
The 500-acre National Stud site on the outskirts of Newmarket supports the thoroughbred breeding industry, with five stallions currently based there.
They include former Group One-winning racehorses Toronado and Dick Turpin.
"This is an isolation unit and we've taken every necessary precaution," managing director Brian O'Rourke told BBC Radio Cambridgeshire.
"The staff at the unit do not go to the main farm which is a good mile and a half from the isolation unit.
"We are hopeful that if we have no more setbacks, hopefully with consultation with a team of vets and the animal health trust, we've got a second gate that we might be able to open up the Stud in time for the start of the breeding season around 15 February.
"That one isolation unit is shut down for 30 days automatically.
"With having 3,000 racehorses on our doorstep in Newmarket, six stallion stations and all those having a lot of mares coming in from overseas and domestically, we have to be seen to set the standard and that's why we're taking all the necessary precautions - to protect all the animals around Newmarket and the general area."
The venue is also closed for public tours until further notice.
O'Rouke continued: "We purposefully (closed our doors to the public) for the simple reason that we're afraid a lot of people that come on the tours or to the coffee shop would stroll out, pat an animal and then go home and do the same to their ponies or whatever horse they had at home or visit a racing yard.
"This is a highly-infectious disease and we have to take every precaution possible and we did that and did it quickly."