Standing in for Nicola Sturgeon at the Scottish Government’s daily briefing, Mr Swinney said that “we have seen the effect of Christmas within the case numbers and that will largely be presenting itself within our hospitals today.”
He added: "The challenges that we are facing will be a product of the development of cases, the immediate aftermath of that rapid acceleration that we saw after Christmas.”
Professor Jason Leitch added: "I think we've now seen first generation infections from Christmas in the numbers and now in the hospital and ICU admissions and now unfortunately in the deaths.
“The challenge here of course is second and third generation infections.
So if you mixed that Christmas, got infections and then spread it further - that is our big danger, that's why the restrictions and the safety measures stay in place.”
The national clinical director said that data in the last week was “encouraging”, adding that the reduction in the R-number suggested that the virus was “decelerating.”
Earlier at the briefing, Mr Swinney said Scotland has recorded 89 deaths from coronavirus and 1,636 positive tests in the past 24 hours.
It brings the death toll under this measure – of people who first tested positive for the virus within the previous 28 days – to 5,468.
Mr Swinney added that 168,219 people have now tested positive in Scotland, up from 166,583 the previous day.
The daily test positivity rate is 7 per cent, down from 7.5 per cent on the previous 24 hours.
He said the number of infections occurring remained “concerningly high”, but added that 334,871 people have received their first dose of a coronavirus vaccine.
This shows the current lockdown measures are “at the very least helping to stabilise case numbers”, the Deputy First Minister added.
Of the new cases, 510 are in Greater Glasgow and Clyde, 328 in Lanarkshire, and 182 in Lothian.
There are 2,004 people in hospital confirmed to have the virus, up one in 24 hours, and 161 patients are in intensive care, up five.