The three cases were found among asymptomatic passengers who flew into Aberdeen on the BA1312 flight from London Heathrow on Friday.
Contact tracing of other passengers on the flight is ongoing.
Giving an update at the Covid-19 daily briefing after the first cases of the variant were recorded in Scotland, Ms Freeman said the Scottish Government was doing “everything it can” to contain the variant and identify any possible chains of transmission.
In light of the discovery, Ms Freeman said the “red list” system for quarantining international arrivals was “inadequate”.
Under the system, international arrivals to airports in England must only quarantine in a hotel if coming from a “red list” country, while in Scotland all arrivals must stay in a hotel, with the exception only of only those coming from within the common travel area.
The red list includes Brazil and neighbouring South American countries.
Ms Freeman said the difference over quarantine requirements in travellers from a red list country was one of the “main areas” where the Scottish Government is seeking to persuade the UK Government to change its policy.
"The Scottish Government has consistently argued that the red list as the sole means of introducing and providing managed quarantine is inadequate, and why we continue to argue that it should be for all international arrivals,” she said.
"One of the reasons for that is that, as you've heard, the virus mutates, and it can be mutating in any country.
"It's not enough just to single some out as really critical, it could be elsewhere. And of course if genomic sequencing is not where we need it to be across the globe … then that doesn't help manage the risk either.
"Every time we have those four-nations discussions, whether it is me as a four-nation discussion with my colleague health ministers, or one that involves the First Minister, we continue to make the point that our control of our international borders is a critical step in managing the risk of coronavirus and bringing down the levels here in the UK.
"That continues to be our main argument, if you like, our main area that we seek to persuade the UK Government. And we will keep on doing that.”
The health secretary said she agreed with comments from Devi Sridhar, chair of global public health at Edinburgh University, who responded to news of the Brazil variant in Scotland on Twitter on Sunday.
"Why robust testing and quarantine policies are needed for international travel given number of circulating variants,” said Prof Sridhar.
"And why just 'red-list' country approach doesn't work (flew from Brazil via Paris and London). Hopefully quickly contained in this instance.”
Prime Minister Boris Johnson said in response to news of the Brazil variant in the UK – with three cases also identified in England – that the UK has “one of the toughest border regimes anywhere in the world”.
Asked if the Government was too slow to implement quarantine hotel measures, he said: “I don’t think so – we moved as fast as we could to get that going.”
Labour leader Sir Keir Starmer said the discovery of the Brazil variant showed the Government had not “secured our borders in the way we should have done”.
He said: “It demonstrates the slowness of the Government to close off even the major routes, but also the unwillingness to confront the fact that the virus doesn’t travel by direct flights.
“We know from last summer that a lot of virus came in from countries where it didn’t originate in, but people were coming indirect and that’s the way people travel.”
Ms Freeman said on Monday there was “no reason” to believe the Brazil variant, known as “P1”, was in circulation in the the community in Scotland.
"I want to stress that there is currently no reason to believe that the P1 varient of the virus is in circulation in Scotland,” she said.
"However, I hope this summary reassures you that we are doing everything we can, and everything that is necessary to check whether this variant of the virus could have been transmitted within Scotland, and to identify any possible chains of transmission.
"These three cases remind us once again how careful we need to be in guarding against new variants. That is why the Scottish Government has put in place such strong travel restrictions.”
Concern has been raised the Brazil variant may be able to re-infect people who have already had another strain of Covid-19.
Lawrence Young, professor of molecular oncology at Warwick Medical School, said in response to the identification of cases of the variant in the UK: “Recent reports from Manaus in Brazil, where the P1 variant is fuelling a surge in infections, suggest that this variant is responsible for re-infecting individuals who were previously infected with a different variant of the virus.
"That’s why it’s even more important to do everything to stop the spread of this virus and all other variants including strict border controls and an efficient test, trace and isolate system.”
The variant has already been discovered in other countries in Europe, including Belgium, Italy and Switzerland.
Dr Deepti Gurdasani, epidemiologist at Queen Mary University of London, said the current situation in the UK “highlights failures in quarantine policy”.
She told BBC Breakfast: “Sage has advised that, unless we had a comprehensive, managed quarantine policy at our borders, something like this would happen.
“But unfortunately it’s something that we’ve been quite complacent about. Now we’re just seeing the consequences of that.”