The measure will allow venues to claim financial support and reduce losses, Deputy First Minister John Swinney said.
The Scottish Night Time Industries Association (NTIA) said while it was “regrettable” clubs would be closed, the requirement was a “pragmatic compromise” that would unlock more support.
It comes as businesses and opposition leaders called on the Scottish Government to relax its Covid-19 restrictions after early research studies suggested Omicron may carry a lower risk of hospitalisation than the Delta variant.
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From December 27, hospitality and leisure settings will need to operate table service and maintain a one metre distance between groups of customers.
Events will also be limited to 100 people standing indoors, 200 people seated, or 500 people outdoors.
While nightclubs will still be allowed to choose to remain open if they comply with these rules, apart from this they will be required to close.
This may allow businesses to gain further financial support and reduce losses, Mr Swinney told the Covid-19 recovery committee on Thursday.
The measure will take effect from 5am on December 27, and will be reviewed after three weeks on January 11.
“Having engaged with the sector, we now propose to require that nightclubs should not operate as such for this three-week period," Mr Swinney said.
"While it would be open to them to operate with distancing and table service, and that option will remain, we consider that closure in regulations, combined with financial support, may reduce losses and help these businesses weather what we hope will be a short period until they are able to operate normally again.
"The Scottish Government is acutely aware of the financial implications for many businesses. We will work with the nightclub industry to develop targeted financial support for businesses that will now be required to close."
The rules around social distancing and table service would “prevent most nightclubs from operating in a way that was commercially viable”, Mr Stevenson said.
He added: “Scottish Government's announcement today provides additional support for those nightclub premises who are unable to repurpose and trade as a bar, while also allowing those who can repurpose to stay open.
"This represents a pragmatic compromise, and we are grateful to ministers and civil servants for taking the concerns of the sector into account and committing to additional funding for those businesses.”
Scottish Conservative Covid-19 recovery spokesman Murdo Fraser labelled the closure a “further setback to a sector already on its knees”.
“I understand that this is a fast-moving situation but, when announcing this enforced shutdown, John Swinney should have spelt out the exact details of the support package that will be given to nightclub businesses, rather than merely promising an update on allocation ‘as soon as possible’,” he said.
“That’s not good enough. Businesses on the brink need to know now exactly what financial support they will receive, and when.
“The SNP Government has been given an extra £440 million in assistance from the UK Government. They need to get that money out the door and into the hands of beleaguered Scottish businesses immediately.”
The Scottish Conservatives have called on the Government to ease current restrictions in light of new research, suggesting the Omicron variant may be milder than Delta.
Omicron may present a two-thirds lower risk of hospitalisation than Delta, a ground-breaking study led by researchers from Edinburgh and Strathclyde Universities and Public Health Scotland reported on Wednesday.
Researchers stressed the results, while “encouraging”, are based on limited early data and have yet to be peer reviewed.
Even if the lower risk of hospitalisation continues, a large wave of Omicron cases still has the potential to put “serious strain” on the NHS, they said.
But Scottish Tories leader Douglas Ross called on Nicola Sturgeon to reduce the isolation period in Scotland from ten to seven days for vaccinated individuals, if two negative lateral flow tests are recorded.
“Doesn't this report just published last night give us the basis to change the rules now, and avoid threatening the viability of essential service and our economy?” he asked Ms Sturgeon at First Minister’s Questions on Thursday.
But Ms Sturgeon said while the results were “encouraging”, it was too soon to change advice.
"We need to take care at this critical moment, because if we allow the spread of Omicron to get too far ahead of us then even if it is significantly less severe, that is going to overwhelm us,” she said.
"Anything we do right now that risks increasing cases, such as removing or weakening self-isolation rules too quickly actually could be seriously counterproductive just at the point where we do see some really good news on Omicron.”
It comes as figures show the use of the Check in Scotland tracking service has dropped significantly in recent months.
The average number of check-ins per day is now almost 65 per cent lower than at its peak in June, according to figures obtained by the BBC.
Collecting customer details for contact tracing is still mandatory in many settings, but businesses are allowed to use different methods, such as taking details when bookings are made, or asking customers to fill in a manual form.
Asked about the issue on Thursday, Mr Swinney told the committee: "It's absolutely vital and we reiterated that point in the First Minister's statement, we reiterated that in the obligations we are putting on venues to make sure the check-in arrangements are visible and complied with.
"The whole check-in arrangement is absolutely crucial to enable us to interrupt the transmission of the virus."