The latest changes will affect about 660,000 people and means that about 1.6 million people in Scotland – almost a third of the population – are now living under enhanced household restrictions.
The restrictions came into effect at midnight and will be reviewed in seven days.
It means people living in the North and South Lanarkshire council areas cannot visit other households or let visitors into their own homes. It follows similar restrictions brought in for Glasgow, East and West Dunbartonshire and East Renfrewshire.
It came as another 175 people in Scotland tested positive for the virus. Ms Sturgeon warned the continued restrictions across the country were vital to avoiding another natinal laockdown.
Also yesterday, health secretary Jeane Freeman said the NHS in Scotland would remain on an emergency footing until at least the end of March 2021.
And Ms Sturgeon said that working from home was expected to be the “default position” for the foreseeable future.
Since 4 September, 205 positive cases of Covid-19 have been identified by Test & Protect teams in Lanarkshire. There were 39 news cases recorded yesterday.
The rule changes mean people should not meet with anyone from other households in indoor household settings, whether in the affected local authority areas or elsewhere.
Ms Sturgeon said: “It is clearly regrettable that these restrictions need to be extended to people living in Lanarkshire. I understand that this will not be welcome news for people living in these areas, especially ahead of the weekend, but we must act now to protect people and get more control over the virus.
“Local public health teams have looked at where cases are being identified and, by restricting indoor meetings, we are helping to protect those who are most at risk from Covid-19 – as they are more likely to be meeting others in a household setting rather than in a public setting.
“I would ask everyone in the affected areas to be extra vigilant, to follow all guidance and to isolate and book a test if they have any symptoms.”
Members of up to two households, to a maximum of six people in total, can continue to meet outdoors, including in gardens, and in hospitality settings. But unlike in England, Ms Sturgeon said that children under the age of 12 would not count towards the limit when two households meet.
Households who have formed an extended household and people providing care and support – for example caring for an elderly family member or delivering shopping – can continue to meet indoors with enhanced hygiene measures in place.
People living in all affected local authority areas who were previously shielding are asked to be particularly vigilant.
Ms Sturgeon said provisional figures show NHS Greater Glasgow and Clyde was the health board area with the highest rise in cases in the past 24 hours, up by 80, while there were 24 cases in NHS Lothian and 12 in Ayrshire and Arran.
Giving further information on the daily coronavirus statistics, she said the new cases across Scotland are 2.7 per cent of people newly tested, up from 1.9 per cent on Thursday.
The First Minister said no more deaths of confirmed patients have been recorded in the past 24 hours and this figure remains at 2,499.
There are 269 people in hospital confirmed to have the virus, up by three in 24 hours. Of these patients, eight were in intensive care, a rise of one.
Speaking about the decision to delay easing lockdown restrictions, including a delay to a proposed return of fans to football stadiums, Ms Sturgeon said: “Over the past month-and-a-half the average number of cases recorded in Scotland has been more than trebling every three weeks.
“That is not sustainable if we are to keep schools and businesses safely open.
“So we have to act now in order to try to stem that increase and avoid more restrictive measures becoming necessary later.”
Ms Sturgeon also spoke about the new limits on gatherings, which will mean people should meet in groups of no more than six, from a maximum of two households. She said: “I know that is a really tough restriction.
“I want to assure you the decision we made on this wasn’t taken lightly. At the moment we believe this is necessary to try to limit and restrict as much as we can the transmission of the virus between different households.”
Ms Sturgeon also said more than 600,000 people have now downloaded the Protect Scotland mobile phone contact tracing app, but added that for it to be as effective as possible “we need as many people across Scotland to download it and use it”.
She said the new app would enhance the existing contact tracing system, saying it could give “almost immediate notification” to people if someone they had been in contact with had tested positive.
Ms Sturgeon said the numbers signing up to use the app had been “excellent” and “probably beyond our initial expectations”.