The new strain of the virus has been found in South Africa, Botswana, Israel and Hong Kong, but no cases have yet been reported in the UK.
Little is known about the variant, but the four nations of the UK have taken the decision to add South Africa, Botswana, Lesotho, Eswatini, Zimbabwe and Namibia to the travel red list as a precaution.
Speaking to Bauer Media ahead of the start of the SNP conference on Friday, Ms Sturgeon said: “I don’t think we should get ahead of ourselves and I don’t think we should be pressing the panic button around any of this.
“But there is no doubt that developments in the last 24 hours around this new variant are the most significant and the most concerning that we have had in the last few months.
“We still need more data, more analysis. We’re monitoring it very carefully, but given the level of concern about the potential of this new variant, we’ve taken highly precautionary action in restricting travel and asking for self-isolation of people coming from certain countries.
“That’s the appropriate action to take at this stage, but we will be looking carefully at developments over the days to come.”
Meanwhile, people aged over 40 will be able to book a booster jab of the Covid-19 vaccine from Saturday, the Scottish Government has announced.
An online portal already open for those aged between 50 and 59 has been expanded to take bookings from the 40-49 age group.
Appointments will be available from November 30, but six months must have passed since the second jab was given.
Those aged 16 and 17 will also be able to book their second dose using the same portal from Tuesday.
Health secretary Humza Yousaf said: “We have now delivered more than 1.5 million boosters and third doses and the excellent progress with the autumn/winter vaccination programme now allows us to invite people aged 40 to 49 to book online.
“Boosters are just as important as the initial vaccinations. Six months after the second dose, immunity levels wane with increasing risk of further infection.
“The booster dose improves your level of protection significantly and is the best way to protect your health and those around you.
“We encourage all those eligible to arrange their appointment via the portal or phoneline for 24 weeks after their second dose.
“I am pleased that, from Tuesday, 16 and 17-year-olds can also use the portal to book their second dose.”
Mr Yousaf went on to say the rollout through the winter would move “as quickly as possible”, with up to 7.5 million doses of Covid-19 booster and flu vaccines due to be administered in the coming months.
So far 1,568,535 people across Scotland have been given a booster, according to official figures released on Friday, with 4,343,208 people having had a first dose and 3,944,225 a second.