Authorities believe cross-contamination in the laboratory may have been behind the positive readings and the results of fresh tests are expected today.
The horses, all flown in from the United States on March 23, are said to be healthy and showing no signs of disease.
MAF Biosecurity New Zealand (MAFBNZ) said the horses had tested negative in the US before export in the US but had since given the positive result.
"There is a strong indication that cross-contamination in the laboratory was the reason for the positive results," said MAFBNZ Import Standards Group Manager Clive Gower-Collins.
"The laboratory will be conducting further tests over the weekend to confirm that this is so. Further investigations will also be made to ascertain how the tests in New Zealand became contaminated.
"The horses have been in quarantine since their arrival from the United States in a secure facility, so there is no risk to the New Zealand horse population."
MAFBNZ said it was confident the weekend testing would confirm the horses are free of the disease.