It comes after NHS staff began to receive the jab on December 8.
So far, more than 5,000 vaccinators and other key staff have had their first dose of the vaccine.
The focus is now on care home residents and staff, who are in the highest-priority group identified by a UK-wide committee.
The development comes as several care homes deal with Covid-19 outbreaks.
The Procurator Fiscal is now investigating seven fatalities at Inchmarlo House Care Home, near Banchory, in Aberdeenshire, and nine at Deeside Care Home in Cults.
More than 140 positive Covid cases have been recorded in residents and staff at the two care homes.
Since May, all confirmed or suspected COVID-19 deaths in care homes and the deaths of people believed to have contracted the virus at work, must be reported to the Crown Office with police then carrying out inquiries.
Meanwhile, in Fife, a number of deaths have been reported at Lomond Court Care Home in Glenrothes with 26 residents and 22 staff testing positive for the virus.
Announcing the vaccine development, Scottish Government said a logistical solution had been reached to "pack down" the vaccine from its initial batches to smaller pack sizes which can then be brought into care homes for the elderly.
Pfizer's vaccine must be stored at minus 70C before being thawed out, however it can be transported in an unfrozen state for up to 12 hours.
The Government says approval has been given to transport the vaccine to nearby care homes or vaccination centres nearby with "minimal wastage", as supplies allow.
Health Secretary Jeane Freeman said: "This is another important moment in our journey through the coronavirus pandemic and I am delighted that we have received the authorisation we need to enable us to vaccinate the most vulnerable people in our care homes.
"Officials in the government and our health boards, along with Pfizer, and the MHRA, have worked really hard to allow this to happen and it is another step on the road to our collective recovery and a return to a more normal way of life.
"We are providing the vaccine to people in care homes according to the order of priority set out by the Joint Committee on Vaccination and Immunisation (JCVI) and we will work through that order of priority as quickly as vaccine supply allows."
She continued: "We are hopeful that subject to further stringent approvals, other vaccines may meet MHRA approval for supply - for example, AstraZeneca and Moderna - enabling more vaccinations to take place at a faster rate.
"In the meantime it remains vital that we all stick to the published restrictions and follow public advice to keep suppressing the virus to as low a level as possible."
There are 23 sites in Scotland which will serve as vaccination hubs for priority groups.
NHS boards will be required to develop their own vaccination plans in each area of Scotland.