And vaccine experts warned this may be a “long way off”, with factors like uptake and the approval of other vaccines set to play a role.
Holyrood's Covid-19 committee heard on Thursday the prospect of a so-called "herd immunity" effect – as the vaccine is widely dispersed – is unlikely to have any impact in the early months of next year.
Experts from the Joint Committee on Vaccination and Immunisation (JCVI), which advises on priorities for vaccination roll-out, as well as the Medicines & Healthcare products Regulatory Agency (MHRA) were among those giving evidence remotely to the committee.
Liberal Democrat MSP Beatrice Wishart asked how many people would have to be vaccinated "before it's safe to reduce any restrictions”.
Professor Wei Shen Lim, chair of COVID-19 Immunisation, Joint Committee on Vaccination and Immunisation (JCVI), said the vaccine would need to be widely dispensed before this could happen.
"It's generally estimated that if a vaccine was highly effective in blocking transmission - maybe 70, 80 or 90 per cent effective in blocking transmission - then given the transmissibility of this coronavirus, one might need to vaccinate up to 70 or 80 per cent of the population," he said.
"That's one estimate that's been given. This is the herd immunity.
"It's very high level of vaccine uptake that will be required to completely stop transmission of the virus through the population."
The vaccine roll-out got underway in Scotland last week. More than 18,000 people north of the Border have now received the first of the two-jab inoculation.
Professor Andrew Pollard of Oxford Vaccine Group, whose candidate vaccine is with regulators awaiting approval, said that as the vaccine is rolled out, transmission levels will fall.
He described the "herd immunity" effect as increasing the level of the population protected to the point where the virus can no longer transmit.
"That's a much bigger ask then being able to show some impact on transmission of the virus," he said.
"But I would expect once we've got a decent number of people vaccinated in the population we will see less transmission. That's going to be really important for getting back to normal.
"But I am concerned that we don't focus entirely on herd immunity at the moment because it may mean that we need 80-90 per cent of people vaccinated in order to get even close to that. And that's still quite a long way off."
He added: "We won't stop the virus completely in the first few months of next year."
Dr Christian Schneider, chief scientific officer at the National Institute for Biological Standards and Control, Medicines & Healthcare products Regulatory Agency (MHRA), told Nationalist John Mason that he could not provide a date when the while population will be immunised.
He said it remained unknown if a number of vaccines in development would succeed or whether others with the regulator would be approved, while uptake would also play into this.
"There’s a lot of factors playing into this and this is why in my personal opinion, it is difficult to to come with an exact date,” he said.