"The mosquito that spreads the virus is not found in the UK, and in any case would not be able to establish in Scotland because of our climate.
"Zika cannot be spread through person-to-person or airborne contact."
He added: "We have already informed the at-risk groups about the risks and how to protect themselves through Health Protection Scotland's travel advice.
"We continue to closely monitor developments in our understanding of the Zika virus as treatments and testing regimes develop."
Since the Zika epidemic began in 2015, nearly 5,000 cases of microcephaly have been recorded in affected regions.
On February 1 this year the World Health Organisation declared the epidemic an international public health emergency. Worldwide concern has centred on north-east Brazil but more than 20 other countries have now been affected.
So far more than 1,650 Zika infections have been reported in the US - four patients in Florida who have tested positive for the virus appear to be the first cases not linked to travel outside the US mainland.
