The First Minister added that while it would be a last resort she remains “open minded” to restrictions at the border with England.
It comes after the first cases of Omicron were identified in the UK on Saturday, and Prime Minister Boris Johnson announced the return of mandatory face coverings in on public transport and in shops in England.
Scotland has so far aligned with the other UK nations in adding ten African countries to the travel red list.
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Speaking on the BBC’s Andrew Marr Show on Sunday, Ms Sturgeon said these measures may need to go further.
She said: “It's important to get a proportionate response to this. I think we may have to go further on restricting travel in the days to come.
"I hope I'm wrong about that, but we must keep our minds open to that.”
Asked if she would consider curbs on travel between Scotland and England, she said: “It's very difficult, you know, as well as I do the nature of the border between Scotland and England and the nature of the flows across the border.
"We will do everything we can. We have at times in the pandemic previously advised against travel across the England-Scotland border, that's always a last resort.
"I think we need to be open minded to doing anything required to keep the population safe right now.”
No cases of Omicron have yet been identified in Scotland, Ms Sturgeon said.
But the First Minister said it should be assumed that the variant will arrive to the country, and asked members of the public to “behave right now as if this new variant is present in Scotland”.
She refused to rule out another ban on indoor mixing between households, although she was clear that “none of us want to go back” to those kind of restrictions.
“We’ve lived with this now for almost two years, we are all sick and tired of it,” she said.
But she continued: “I’m not going to sit here, 48 hours on from the detection of a variant of this virus that may be even faster transmitting than Delta – and Delta was faster transmitting than anything that came before – that may escape vaccines to some extent, I’m not going to sit and rule anything out.
Ten countries have so far been added to the UK travel red list: South Africa, Botswana, Lesostho, Eswatini, Zimbabwe and Namibi, Malawi, Mozambique, Zambia, and Angola.
New rules also require fully vaccinated arrivals to take a PCR test within two days of arrival and to self-isolate until a negative result is received.
While mandatory face coverings will be re-introduced to England, UK health Secretary Sajid Javid said it is “nowhere near” time to reintroduce social distancing rules and work-from-home guidance south of the border.
He told Sky on Sunday: “We know now those types of measures do carry a very heavy price, both economically, socially, in terms of non-Covid health outcomes such as impact on mental health.”