It comes as people over 45 in England were invited to begin booking vaccination appointments on Tuesday.
Asked when Scots in the same age group will be offered a vaccine, Ms Sturgeon told a Covid-19 briefing on Monday that this will begin “in the next few days".
Chief Medical Officer Dr Gregor Smith added: “The planning is already underway for that.”
"People will start to receive invitations across Scotland very soon, in terms of being invited to come and get their vaccines,” he said.
The Scottish Government has “effectively” hit its target of offering a first dose to all over 50s and those with underlying health conditions by April 15, the First Minister said, with a small proportion of that group still to receive a jag – including herself.
Ms Sturgeon said that while some people may have “fallen through the cracks,” this is inevitable in any large-scale programme.
Some 96 per cent of those aged 55 to 59 have been given a vaccine in Scotland, along with 84 per cent of those aged 50 to 54. Dr Smith asked those at particular risk to make sure they come to their appointment as soon as possible in the next phase of the rollout.
“Males in particular, and those from BAME communities and people who have a BMI above 30, we would particularly encourage all of those groups to take a vaccine as quickly as possible,” he said.
"We know that, as well as age being the most defining characteristic of risk, these are additional risk groups which we would want to be receiving their protection as quickly as possible.”
It comes as the Joint Committee on Vaccination and Immunisation published its finalised guidance for phase two of the vaccination programme on Tuesday.
The committee recommends that the programme continue in descending age order, with a particular emphasis on vaccination of men, minority ethnic groups, socio-economically deprived groups, and those who are obese.
Ms Sturgeon asked those marking Ramadan to still accept their vaccine, after faith leaders said the jag does not count as breaking the fast.