The First Minister told MSPs on Thursday that Linzi Page's case meets the "compassionate exemption" that is part of the new ban, which will come into force across Scotland on Friday.
The ban prevents people from travelling in and out of areas under level three and four restrictions. It prompted Ms Page, who is based in Fife, to fear that she could not travel to Edinburgh Airport for her trip next month.
She is planning to take her seven-year-old son Calan and four-year-old daughter Charlotte on holiday and wrote to Ms Sturgeon about her dilemma last night. And after the issue was raised at First Minister's Questions by Labour leader Richard Leonard, Ms Sturgeon confirmed she had already been in touch with Ms Page to reassure her.
"I wrote to Linzi this morning clarifying the situation," Ms Sturgeon told MSPs.
"She wrote to me last night outlining her situation, which is indeed tragic and my heart goes out to her as I'm sure the heart of each and every one of us does.
"She asked me for clarity on whether she can go on a final holiday with her family. I have written back to her today advising her that under regulations anyone in a situation like hers can go on a final holiday."
The travel regulations will come into law tomorrow, but contain a number of exemptions where people have a "reasonable excuse", including travel for work purposes.
Ms Sturgeon said: "There should be no doubt that Mrs Page would absolutely meet that exemption because one of the explicit examples given on the face of the regulations is travel for compassionate reasons which relate to the end of a person's life.
"Linzi's situation is tragic, but on both compassionate and indeed on legal grounds she can go on her holiday and I wish her and her family well."
Mr Leonard welcomed the First Minister’s intervention, but said the majority of Scots were struggling to keep with the regulations on Covid restrictions.
"The best-case scenario as it stands is that this travel ban confuses them – the worst-case scenario is that it will criminalise them,” he said.
"The travel ban is a red herring.”
He called for immediate action to improve the Test and Protect system and appropriate PPE for NHS staff and greater safety in schools.
"It is in all of our interests for the Government to get this right – so First Minister, will you admit that you have not got this right and before it’s too late will you re-think the travel ban and its application?” he asked.
But Ms Sturgeon insisted she was taking the action she considered necessary to keep the country “as safe as possible”.
"It is absolutely incumbent on somebody like me to do my level best to do the right things and the necessary things – even if they’re not always popular or welcome,” she said.