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A leaked letter from Robin Swann to his counterpart in the Republic of Ireland has exposed major flaws in how visitors from Covid-19 high risk countries are monitored after crossing the border.
It flags up "serious impediments when it comes to enforcing or monitoring" those required to self-quarantine.
Mr Swann said "we have no way of tracing them for spot checks" if they fail to complete a locator form.
He called for a "rapid solution".
Mr Swann also said closer co-operation between both governments was needed, which could involve new "legislation and data-sharing agreements".
"I believe this would be a significant achievement which would demonstrate our commitment to working together to effectively address common challenges" Mr Swann wrote.
Under the current arrangements, international visitors arriving in the Republic of Ireland before travelling onwards to Northern Ireland must complete a locator form within 48 hours of crossing the border.
They must also self-quarantine for 14 days if arriving from a country assessed as high risk.
'Serious impediments'
But in the letter to Irish Health Minister Stephen Donnelly, Mr Swann wrote: "There are serious impediments when it comes to enforcing or monitoring this at present."
He added: "We are reliant on everyone who has travelled into the Republic of Ireland and then on to Northern Ireland completing our passenger locator form.
"If they fail to do so we have no way of tracing them for spot checks to make sure they are quarantining."
Mr Swann then suggested the "logical solution" was to ensure all international travellers who arrive on the island provide data "which is accessible for compliance checks in our respective jurisdictions".
Also in the letter, Mr Swann urged his counterpart in Dublin to address with him "the inability" of their jurisdictions to capture and share information about international travellers moving across the border.
The letter was sent at the start of this week.
BBC News NI has also sought a response to the concerns raised in the letter but has yet to hear back from the Irish government.