Speaking at her daily briefing, Ms Sturgeon said 31 people had died from the virus in the last 24 hours after testing positive.
It brings the total number of Covid-19 deaths by this measure to 4,070.
The First Minister also confirmed that a further 1,001 positive cases had been reported since 9am on Thursday, December 10.
The figure represents 4.6 per cent of all those tested in the previous 24 hours.
Ms Sturgeon said that, in “absolute terms” that figure was the highest it had been in “a little while”, but added that since the test positivity rate was below 5 per cent, the World Health Organisation still considered the outbreak “under control”.
246 of the cases were identified in the NHS Greater Glasgow and Clyde health board area.
196 were in NHS Lothian, and 125 in NHS Lanarkshire.
It means that 104,306 people have tested positive for coronavirus in Scotland since the beginning of the pandemic.
999 people are currently in hospitals across Scotland with the disease, 15 more than yesterday, and 53 of those are being treated in intensive care units.