The Scottish first minister advised against crossing the border after Boris Johnson announced a second national lockdown on Saturday night.
She said that the prevalance of the virus was currently lower in Scotland than other parts of the UK and that restrictions imposed last month "may be starting to slow the rate of increase."
Scotland has a rate of just under 170 new cases of coronavirus per 100,000 population over the last seven days, compared to 355 in Northern Ireland, 261 in Wales and 230 in England.
However Ms Sturgeon warned that Scotland could also increase restrictions under the new five-tier system that comes into effect on Monday.
The first minister said that a decision on lockdown in Scotland would depend on whether the UK government offered additional financial support.
Chancellor Rishi Sunak announced that the furlough scheme will be extended for another month - having previously insisted that it would end on 31 October.
"A crucial point for us is whether support on the scale announced for English businesses is available for Scottish businesses now or if we needed to impose further restrictions later - or if it is only available if Scotland has a full lockdown at the same time as a lockdown in England," Ms Sturgeon said.
Ms Sturgeon said that the Scottish government "will not hesitate" to increase restrictions locally or nationally if necessary.
She added: "People across Scotland have faced significant restrictions since late September as we work to stop the increase in Covid cases across the country.
"Prevalence of the virus is currently lower in Scotland than in other parts of the UK and there are some signs that those earlier restrictions may be starting to slow the rate of increase."
Ms Sturgeon advised the public not to travel to or from any area in Scotland currently in level 3, or to other parts of the UK that are now at higher levels of restrictions.
She said: "Following today's announcement by the prime minister we are also asking that people do not travel to England, or from England into Scotland unless absolutely essential, just as we are also asking people not to go to Northern Ireland or to Wales.
"We know that these restrictions are difficult, but public health and preventing the spread of the virus must come first."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies