Gatherings of more than 500 people should be cancelled from next week, the Scottish government has advised.
First Minister Nicola Sturgeon said this was to free up emergency services, including police and ambulance crews, to deal with the coronavirus outbreak.
She said it was not yet necessary to close schools, but advised all overseas school trips should be cancelled.
There have now been 60 cases of Covid-19 confirmed in Scotland - a rise of 24 from Wednesday.
NHS Lothian has the highest number of cases with 11. NHS Greater Glasgow and Clyde has 10.
The first case of coronavirus transmitted within the community was detected in Scotland on Wednesday.
Ms Sturgeon confirmed the UK had now entered the delay phase of controlling coronavirus which would mean a change in guidance.
From Friday, people with coronavirus symptoms should stay at home for a period of seven days. They should not call their GP or NHS 24 unless their condition deteriorates.
The first minister said the advice on mass gatherings was a Scottish government decision designed to reduce the impact on the emergency services, rather then preventing the spread of the virus.
"We know that certain events have an impact on our policing and frontline health services," she said.
"Our health services in particular will be under acute pressure in the weeks and months to come. I think it is incumbent on the government to do what we can to remove unnecessary burdens on our public services."
Ms Sturgeon said she also wanted to send a clear message that the outbreak should not be treated as "business as usual".
How is coronavirus affecting Scotland?
- The Scottish Green Party has cancelled its spring conference
- Offshore oil and gas industry says installations will be placed on immediate "lockdown" if a worker on board tests positive for coronavirus
- The VisitScotland Expo in Aberdeen, due to take place on 1 and 2 April, has been cancelled after a "significant number of cancellations"
- Loganair has announced a reduction in its flights after a "marked drop" in bookings
- The Courier newspaper has cancelled its annual Menu Food and Drink Awards ceremony
- The Who concert in Glasgow on 23 March is off after the band postponed its UK tour
Another new measure announced by the first minister was the cancellation of all school trips.
But she said that schools, colleges and universities would remain open as their closure would have a "very direct affect on the ability to keep key workers at work".
There are also concerns that young people would instead gather in informal settings where the risk of spreading the virus was higher.
Ms Sturgeon said "complex judgements" needed to be made around school closures as they could potentially last until the end of the summer term.
"If it gets to a stage where the advice is to close schools, this will not be for a week or two weeks," she said.
"This would be something that was advised to last throughout the peak of this infection and that is potentially until the summer period."
The matter would be kept under "very close" review, she added.
The global outbreak has now been labelled as a pandemic by the World Health Organization.
There are 590 confirmed cases across the UK and 10 people have died - all of them in English hospitals.
Scotland's national clinical director, Jason Leitch, has defended the approach taken so far, saying that the UK authorities had not been "complacent".
In a tweet, he wrote: "For those in equal number suggesting we're overreacting and not acting fast enough we are doing neither.
"The balance of which population interventions and their timing is crucial. We are not complacent."