Scottish Health Secretary Nicola Sturgeon said the pair were recovering well in a Lanarkshire hospital.
The Foreign Office is advising against all but essential travel to Mexico.
This comes after the World Health Organization raised its alert level for a possible pandemic, saying there was sustained human-to-human transmission.
The couple receiving treatment in Scotland are described as not being particularly ill.
Ms Sturgeon said: “I would reiterate that the threat to the public remains low.
“The precautionary actions we have taken over the last two days have been important in allowing us to respond appropriately and give us the best prospect of disrupting the spread of the virus.”
Of 25 cases reported in the UK, 14 are still being investigated.
All 14 were well enough to be managed in the community, Health Secretary Alan Johnson told MPs.
The WHO has raised its alert level over swine flu from three to four – two steps short of declaring a full pandemic.
WHO Assistant Director General Dr Keiji Fukuda said it signalled a “significant step towards pandemic influenza”, but added “we are not there yet”.
The EU health commissioner had already warned UK tourists against travelling to Mexico and other directly affected areas.
But the UK Foreign Office changed its travel advice on Monday after the WHO raised its alert level.
Mexican Health Minister Jose Angel Cordova said on Monday that 149 people had died after contracting suspected swine flu.
However, there have been no deaths elsewhere.
The Department of Health (DoH) has said surveillance arrangements are being “stepped up” in the UK.
Among the UK cases was a 62-year-old female Canadian visitor to Sale, Greater Manchester, who was taken to hospital as a precaution after showing flu-like symptoms.
NHS Northwest says the tests on the woman in Manchester have proved negative, and her case has been downgraded to being an unspecified viral infection.
Mr Johnson also said the government proposed to use its stockpile of anti-viral drugs to treat patients showing symptoms of the disease, should the virus start spreading in the UK.
He added: “People will wish to know whether they should wear facemasks.
“Although we are aware that facemasks are being given out to the public in Mexico, the available scientific evidence does not support the general wearing of facemasks by those who are not ill, whilst going about their normal activities.”
And Mr Johnson said preparations had been going on to cope with a flu pandemic for the last five years.
“We have established a stockpile of enough anti-virals to treat more than 33 million people, that is to say half of the UK population,” he said.
There are fears that the virus has begun to spread around the world:
- There are 40 laboratory-confirmed cases of swine flu in the US, 26 in Mexico, six in Canada and one in Spain, the World Health Organization (WHO) said on Monday
- Tests are also being carried out on individuals or groups in New Zealand, Australia, Brazil, Britain and Israel who fell ill following travel to Mexico
- The United States and the European Union have urged travellers to Mexico to exercise caution
- WHO experts have raised the global pandemic alert level from three to four on a six-point scale
EU Health Commissioner Androulla Vassiliou said: “I’d try to avoid non-essential travel to the areas which are reported to be in the centre of the cluster in order to minimise the personal risk and to reduce the potential risk to spread the infection to other people.”
England’s Chief Medical Officer Sir Liam Donaldson said a potential pandemic would mean “many many more people becoming ill than occur every winter with the normal seasonal flu”.
He added: “If a new pandemic does start as a result of this outbreak in Mexico and the United States, we can’t make it go away, but what we can do through our plans, particularly our stockpiles of anti-virals, is mitigate its effect.”
UK Foreign Secretary David Miliband said it was “right that we put the issue of swine fever on the foreign ministers’ agenda” because there needed to be “maximum European co-ordination” on the issue.
The Health Protection Agency (HPA) has a procedure for confirming whether or not a patient has swine flu.
If a patient rings their GP or NHS Direct to report symptoms, they will be told to stay at home, not to visit a surgery or hospital.
The HPA has prepared an “algorithm” – in essence, a flow chart – for suspected cases. On the phone, or possibly even face-to-face depending on the circumstances, the patient’s GP or NHS Direct will take the patient through the algorithm.
If the answers to the algorithm lead the questioner to believe the patient may have swine flu, a sample will be taken that will then be sent to one of the HPA’s network of regional labs for testing.
If the sample is confirmed as influenza type A, it will then be sent to the HPA’s Reference Lab at the Centre for Infections in Colindale, where they will carry out genetic typing on it and establish whether it is a confirmed case of swine flu.
There have also been cases of swine flu reported in Canada and a suspected case in France.