Jeane Freeman also confirmed that Scotland would receive 44,000 doses of the Oxford University and AstraZeneca Covid-19 vaccine at the beginning of next week with the four nations continuing to plan supply and delivery.
After this second vaccine's approval on Wednesday, the Scottish Government announced it would be given to people north of the border from Monday, January 4 along with the rest of the UK nations.
However, speaking to the BBC's Good Morning Scotland Programme today, Ms Freeman admitted they could not guarantee the target of being on track to vaccinate everyone over 50 by the spring without considering the issue of supplies.
Ms Freeman said: "It can't be a guarantee because it depends on supplies but what I do know is that our planning is ready.
"Our modelling and the number of registered vaccinators we have is there.
"As long as the supplies of both vaccines continue to come through to us then we are ready to deliver the vaccine to all of those in that Joint Committee on Vaccination and Immunisation (JCVI) priority list - so that's everyone over 50 - in the spring we will get there as long as those supplies arrive.
"That is very positive and good news because that is a group of people that committee of experts have identified as those who are most at risk of serious illness and death from Covid-19.
"It's really important that we work as hard as we can to make sure that we vaccinate those individuals as quickly as we can."
On Wednesday, Ms Freeman said the priority list for vaccination set out by the JCVI remains the same, with second doses of both vaccines required within 12 weeks.
The Health Secretary also confirmed Scotland has 2,300 registered vaccinators "with the right clinical experience" to help the roll-out, with a view of extending it past care homes soon.
Ms Freeman added: "The next group of people, and the group that AstraZeneca vaccine really opens the door for us to be able to vaccinate easily, are those who are over 80 and live in their own homes, they live in the community not in care homes.
"We'll be doing that through GP practices, pharmacy and local vaccination centres
"But as we go through into larger groups of people, and people who are perhaps more mobile and it's easier for them to get to larger centres, then we'll use those larger centres - but initially the GP practice and the local pharmacy will be the place.
"Also, we'll bring in mobile vaccination centres because large parts of our country, as you know, are remote and rural - it's hard for people to get into towns and so on, so the trick is to take the vaccination to as many people as possible."
Yesterday, Scotland recorded a record high number of 2,045 positive coronavirus cases, however First Minister Nicola Sturgeon commented that the Oxford vaccine approval was “much needed good news on the Covid front” despite “difficult winter weeks ahead.”