The Prime Minister added that although it would be a last resort, she remains “open-minded” in the face of 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 facewear in public transport and in shops in the UK.
Scotland has so far joined the other British nations by adding ten African countries to the travel red list.
In a speech on the BBC’s Andrew Marr Show on Sunday, Sturgeon said these measures may need to go further.
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She said: “It is important to get a proportionate response to this. I think we will have to go further in restricting travel in the coming days.
“I hope I’m wrong about it, but we need to keep our minds open to it.”
Asked if she would consider limiting 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 currents across the border.
“We will do everything we can. At times in the pandemic we have previously advised against traveling across the border between England and Scotland, it is always a last resort.
“I think we need to be open to doing whatever it takes to keep the population safe right now.”
No case of Omicron has yet been identified in Scotland, Sturgeon said.
But the Prime Minister said it was to be assumed that the variant would arrive in 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, even though she was aware that “none of us want to go back” to those kinds of restrictions.
“We’ve been living with this now for almost two years, we’re all tired of it,” she said.
But she continued: “I do not intend to sit here, 48 hours after the detection of a variant of this virus that possibly transmits even faster than Delta – and Delta transmitted faster than anything that came before – that can escape vaccines to some extent I am not going to sit and rule anything out.
Ten countries have so far been added to the UK’s Red Travel List: South Africa, Botswana, Lesostho, Eswatini, Zimbabwe and Namibia, Malawi, Mozambique, Zambia and Angola.
New rules also require fully vaccinated arrivals to take a PCR test within two days of arrival and isolate themselves until a negative result is received.
While mandatory face coverings will be reintroduced to England, British Health Minister Sajid Javid said it was “nothing near” time to reintroduce social distance rules and work from home guidance south of the border.
He told Sky on Sunday: “We now know that these types of measures have a very high cost, both economically, socially, in terms of non-Covid health outcomes such as the impact on mental health.”