The delivery of the Pfizer BioNTech vaccine began on Tuesday, December 8. By Sunday, 18,644 doses had been given.
The first to receive the vaccine were vaccinators themselves followed by the beginning of a rollout in care homes.
Interim Deputy Chief Medical Officer Nicola Steedman gave the first weekly update into the vaccination programme on Wednesday.
She said the arrival of the vaccine represented a “stone of hope” in the “mountain of despair” of the Covid-19 pandemic, quoting Martin Luther King Junior.
“We are entering what we hope is a new phase of the pandemic and one of hope,” she said.
Asked what capacity Scotland had of the Pfizer Covid-19 vaccine, Dr Steedman said she could not give a “magical date” when the programme would be finished.
Scotland does not yet have a full supply of the Pfizer vaccine or any vaccine from other manufacturers, she said, and also faces logistical issues in the delivery of doses.
"Even if we had all of the vaccine that we needed for the whole population, we would still be in a position where it would take months, there's no doubt about that,” she said.
"I think we would still definitely be looking towards spring at the very, very earliest, and that's if everything was was lined up, which realistically is not necessarily likely to happen.”
Dr Steedman said the Scottish Government had lined up the necessary number of vaccinators needed for delivery.
Despite Dr Steedman’s comments around the logistics of vaccine delivery, First Minister Nicola Sturgeon said the main issue facing Scotland was one of supply.
"Nicola is right to talk about all these other complications, but we can factor all of those into our planning,” she said.
"The one uncertainty that we are not in control of is just the pace and the flow of supplies.”
It comes as the Covid-19 vaccine manufactured by French company Valneva entered clinical trials on Wednesday.
The vaccine is being produced at the Valneva factory in Livingston, West Lothian.