But restrictions on indoor events and hospitality will remain until at least January 24, the First Minister said in a Covid-19 update on Tuesday.
While pressure remains on the NHS, the Covid situation in January has been better than predictions feared, Ms Sturgeon said, and the Scottish Government is now working on a framework for “living with” Covid, to be published in the coming weeks.
It comes as 10,392 new cases were recorded on Tuesday, while 1,479 people were in hospital and 54 in intensive care.
Outdoor gatherings of more than 500 people will be permitted from Monday, meaning that upcoming football and rugby matches, including Six Nations fixtures, can take place.
The Covid certification scheme will be tightened, with events of more than 1,000 people required to check the status of at least half of attendees or at least 1,000 people, whichever is higher.
From Monday the requirement to be “fully vaccinated” for this scheme will be increased to three doses for those whose second dose was more than four months ago.
The Scottish Government is also considering extending the scope of this scheme to other settings, Ms Sturgeon said.
Other restrictions, including limiting indoor events to 200 people seated or 100 people standing, and requiring table service in hospitality settings, will remain in place until at least January 24, pending a review of data by ministers.
The advice to the public to limit contact with other households as much as possible also remains.
Ms Sturgeon also announced an extra £5 million of funding to local authorities and childcare providers to increase ventilation.
Scotland has begun to “turn a corner" in its pandemic response, the First Minister said, and the Scottish Government is working on an adapted framework for “living with” the virus to be published in the coming weeks.
This will involve considering what adaptations can be made to life to make things safer for everyone, Ms Sturgeon said.
"Because of the efforts we have all made - we are in a better position than I feared would be the case when additional measures were announced in December,” she said.
"And I hope we are now seeing signs of improvement. That is allowing us to start the process from Monday of lifting the additional restrictions - and I hope that next week I will be able to confirm further steps in that process.”