Mark Drakeford has acknowledged that Wales' new Covid pass system is "vulnerable to abuse".
The passes, which are now compulsory, will show that the individual is double-vaccinated, or provide proof of a negative lateral flow test within the last 48 hours.
People attending nightclubs and other large events such as rugby matches will be required by law to demonstrate a Covid pass from October 11.
However the First Minister has acknowledged that lateral flow tests pose a risk of vulnerability to the new system, with the opportunity to 'fake' a test.
In his Good Morning Britain interview, Mark Drakeford admitted: "This is a vulnerability in the scheme.
“We have created a specific offence which will mean that if someone deliberately falsifies the result of a lateral flow test they will be breaching the law in Wales."
Those who fake a coronavirus test result or vaccination status will be committing a criminal offence and face a fixed penalty notice.
Mr Drakeford continued: "The law will be there and there will be a reckoning.
“The offence is there to deter people – that is the main impact of it. It says to people: ‘This is a serious matter and you you need to take it seriously.’”
Despite the risk, the First Minister said he "doesn't accept" the idea that people will "set out to cause themselves and others harm".
He added: “The broader point for me is that we have literally thousands and thousands of people taking lateral flow tests in Wales every day of the week – they’re not doing it in order to evade the law, they’re doing it to make sure they themselves are safe from coronavirus and they’re keeping other people safe as well.
"I’m quite sure that the huge bulk of people who are attending a rugby match or visiting a nightclub will use the lateral flow devices in exactly this way – not to get round the rules, but to make sure they’re keeping themselves safe from this dreadful disease".
The new measures make Covid passes compulsory for indoor non-seated events for more than 500 people and outdoors ones of more than 4,000. It will also include any setting with more than 10,000 in attendance.
The legislation was passed in the Senedd last week by just one vote, despite opposition from the Welsh Conservatives, Plaid Cymru and the Liberal Democrats.
Some nightclubs in Wales have already made the decision to close their doors early instead of implementing the new laws, saying they believe it is safer and easier.
It is hoped the new measures will cut down on the transmission of the virus and potentially avoid more strict measures coming into force later in the year.
The First Minister explained the Covid pass has been introduced at the highest risk venues to "help them stay open during the autumn and winter".
He added, "it is not to be an extra burden on them or to single them out, but to protect them so they can go on operating successfully as we go into what is going to be a challenging time of year".
Wales is facing some of the highest infection rates since the beginning of the pandemic, particularly among young people.
Economy Minister, Vaughan Gething, said, "The Covid Pass is just one of a series of measures in place to help prevent people spreading and catching coronavirus while helping to keep the economy open".
The Welsh Government will use the current enforcement regimes for monitoring compliance.
A venue could be issued with a fixed penalty notice and a maximum fine of £10,000.
Conservative health spokesman, Russell George, accused the Welsh Government of a U-turn, having previously ruled out introducing them.
He said, "I just do not think that we should become a checkpoint society by introducing a vaccine passport".