Northern Ireland can enforce the 14-day quarantine requirement for anyone travelling from Spain, the health minister has said.
Robin Swann, speaking on the BBC's Good Morning Ulster programme, said people coming into Northern Ireland will have to complete a locator form.
Failure to self-isolate will result in a fine up to £1,000, he said.
The mandatory quarantine on travellers coming into NI from Spain came into effect at midnight on Saturday.
Mr Swann told the assembly on Monday that detailed scientific information he received showed the weekly Covid-19 case rate in Spain had doubled.
Northern Ireland's quarantine mirrors a similar move announced by the UK government over the weekend.
On Tuesday, Mr Swann said that the difference between the quarantine checks system in Northern Ireland and the Republic of Ireland is "we actually have the enforcement".
"Self-isolation in Northern Ireland, and again I suppose the difference that we have between ourselves and the Republic of Ireland - anyone landing who has come from a 'red' country is asked to complete a travel locator form. Failure to do that is subject to a penalty," he said.
"Anybody who completes that form - and most people have to because they will face a financial penalty if they don't - there's then a company that we have engaged along with Public Health England who contact a sort of random sampling.
"So [via] your phone number, you will be contacted then to make sure you still are self-isolating."
Mr Swann said that if you are not contactable, or it is believed after three attempts that you are not self-isolating, then information will be passed, via UK Border Force, to the Police Service of Northern Ireland (PSNI) and the Public Health Agency which will carry out random checks.
"And then again, failure to do that is subject again to a further fine of up to £1,000."
The PSNI told BBC News NI that travel regulations are a matter for Border Force.
"The police role is to respond to reports from the UK Border Force or any of their associated partners of potential breaches," it said.
On Monday, Mr Swann told assembly members that employers would be urged to show flexibility to those having to quarantine and to allow staff to work from home where possible.
He said he had the full support of the executive and mechanisms were now being considered by other departments to help those affected by the restriction.
But the country's prime minister said the UK government decision to impose a 14-day quarantine was "unjust".