However, John Swinney did warn there were some Level 3 areas where rates of the virus remained “stubbornly high”. In Level 4, non-essential shops, restaurants and bars would close.
Mr Swinney, who will update the country tomorrow (Tuesday) also said he hoped there would be “some availability” of the new vaccine in Scotland before Christmas.
Speaking on the BBC’s Politics Scotland programme, he said plans were continuing to ensure a very broad cross section of the population were vaccinated as quickly as possible.
But Mr Swinney warned of a tricky period ahead and said that just because a vaccine was coming, the battle against Covid-19 was not over.
Figures for Sunday showed that 1,159 new cases of Covid-19 were detected in the past 24 hours, with no further reported deaths of people who tested positive for the virus.
However, the number of Covid patients in hospital rose from 1,198 to 1,241 and there was an increase of eight people being treated in intensive care.
Local authorities in the Greater Glasgow and Clyde and Lanarkshire health board areas were warned on Friday they could be placed under the highest level of Covid restrictions.
Ministers are expected to make a decision about restriction levels on Tuesday, with any change taking effect from Friday.
Mr Swinney said there was still “too much human interaction going on” that was enabling the virus to thrive, despite the current restrictions.
He insisted there was little evidence of the virus spreading within schools, adding: “It is within shopping, within hospitality, within the general movement of individuals within society and I suspect probably also within household visiting.”
On news of a vaccine from BioNTech and co-developers Pfizer, which preliminary analysis has shown could prevent more than 90% of people from getting Covid-19, Mr Swinney said the Scottish government hoped to have access to the drug before Christmas.
He added: “We will want to make sure that we can vaccinate a very broad cross section of the population as quickly as we possibly can do.
“Obviously there will be prioritisation given to those that are at the most vulnerable and the most critical level.”