The measure will be eased for places of worship and weddings, civil partnerships and funerals from Monday.
Wedding industry leaders welcomed this earlier easing, but said it had come too late and the damage to the sector “has already been done”.
The law will be replaced by guidance once dropped.
It comes as the number of people in hospital with Covid has reached record levels in recent weeks, though the figure fell slightly on Wednesday to 2,344.
Waiting times performance at accident and emergency (A&E) departments are at their worst ever, prompting warnings of a “patient safety crisis” from the Royal College of Emergency Medicine.
In advance of Ms Sturgeon’s statement, the college said it would “welcome” an extension to the face mask rule to protect the under-pressure NHS.
NHS Ayrshire and Arran issued a warning over high pressure on all its services on Wednesday, urging people to “stop and think” before visiting A&E.
And Unison said staff in NHS Grampian were at “breaking point” over staffing shortages, stress and working extra hours.
The union, which has around 3,000 members in Grampian, said staff were concerned for patient safety.
The Scottish Licensed Trade Association (SLTA) said it was “bitterly disappointed” by the decision to retain face mask rules.
“The lack of use of face coverings is already clearly evident in many settings and this extension of the restrictions will make little difference,” said managing director Colin Wilkinson.
The difference in rules between Scotland and England confuses people, Mr Wilkinson said.
“It is exceptionally unfair for business owners and their staff to have to remind people who are not familiar with our rules that they must wear a face covering,” he said.
“To say we are bitterly disappointed by today’s announcement is an understatement as we still face nearly three more weeks of restrictions.”
The Scottish Chambers of Commerce also said it was “deeply disappointed”.
“Even with the phased approach now announced by the First Minister, Covid rules remain more stringent in Scotland now than in England or Wales and the lack of a four-nations approach is causing concern, particularly its impact on a potentially unequal economic recovery,” said chief executive Dr Liz Cameron.
“Tourism, for example, will be hit by this decision as the prolonging of Covid-19 rules is likely to make Scotland less attractive than other destinations, just as people are starting to think about booking Easter, spring and summer breaks here.”
Duncan McConchie, chair of the Scottish Wedding Industry Alliance, welcomed the earlier easing of face covering requirements for the sector, but said it would come “far too late”.
Since August, wedding guests have been required to wear face coverings during the ceremony, but not the reception, which Mr McConchie said “does not make sense”.
The virus could still spread among guests at the reception, he said, but the rules have meant couples have not been able to take maskless photographs during the ceremony.
“It has been a real issue," he said.
"We’re delighted that they are being removed, but it’s very, very late, and we think a lot of the damage has already been done.”
The wedding industry is in a “really difficult position”, he said, in part due to couples booking venues in other UK nations due to more relaxed Covid regulations.
The Scottish Conservatives said mask-wearing should be down to “individual choice”, and the continued requirement was “really holding some people back”.
Scottish Labour said the cautious approach was “understandable”, but raised concerns over a lack of detailed plans for testing and antivirals for immunocompromised Scots when free provision of lateral flow tests ends in May.
Ms Sturgeon told MSPs the phased removal of mask laws strikes a “balance” between the Government’s desire to remove the last remaining legal measure and the “common sense need for continued caution” during the current wave of infection.
"I recognise that face coverings are an inconvenience,” she said.
"However, given all the sacrifice of the past two years, and in view of the current pressure on the NHS, I believe the vast majority of people will accept that for a further two weeks this is a proportionate precautionary measure while we pass the peak of this latest wave.
"It also provides some further protection to those who are most at risk from the virus.”
The announcement was made on the day it was confirmed both Scotland's Deputy First Minister and his Cabinet colleague, justice secretary Keith Brown, had tested positive for Covid.