He told the coronavirus daily briefing on Wednesday that there are some groups which should be more cautious around the vaccine, which has been approved by the MHRA and is set to begin rollout in Scotland.
"We are not advising that those who are pregnant or who plan to be pregnant within the next three months receive this vaccine at this point in time,” he said.
“The reason for that is the limited amount of data we have on the use of the vaccine in that group just now.
"It may be that over time we are able to develop further information in relation to that but at this point in time we are not advising it”.
Both Dr Smith and First Minister Nicola Sturgeon reassured the public that the vaccine is safe.
"As soon as I can get this vaccine, I will be getting this vaccine,” said Ms Sturgeon.
"My parents and other relatives are likely to be in a higher priority group than I am, and I will be strongly encouraging them to get this.
"I would encourage without hesitation everyone who is eligible, to get this vaccine as soon as they can.
"The processes for authorising these vaccines, has been done admirably quickly and the global scientific community deserves huge credit for this, but no corners of the cut in terms of authorisation to ensure the safety of the vaccines that will be offered to people.”
Dr Smith said: “It’s gone through exactly the same time of scrutiny as any other product.
"The development of the vaccine has been accelerated by a whole variety of circumstance, the combined efforts of the scientific community, and the availability of pre-existing science and research which was able to be deployed into this, and the readily available and eligible cohort of volunteers participating in research trials that allowed us to come to this point as quickly as we have.
“But that scrutiny about the safety and the efficacy of this vaccine is the exact same process which would be applied whether it was Covid or some other vaccine.
"We should all take reassurance that no corners have been cut.”