Arlene Foster told the BBC's The World This Weekend that data could be "sent to the cloud and tracked".
"It's not beyond the boundaries of possibility that we deal with the realities of the situation of today using new technologies," she said.
"I'm thinking of going through technology borders essentially.
"So when people move from Northern Ireland to the Republic of Ireland, they're tracked in relation to technology and that data is sent to the cloud and can then be tracked."
Mrs Foster said she didn't foresee a time when heavy goods vehicles would be stopped and searched at a hard border.
"There is a border in reality, but if you go to any border road, you'll not see a particular sign that says you're leaving or coming into Northern Ireland and that's going to remain the case.
"If there are tariffs imposed, that could be done remotely."
Speaking at her party conference on Saturday, the first minister said Brexit presents the biggest economic opportunity for the UK in decades.
Mrs Foster also criticised the Irish government for allowing "political instability in Dublin" to drive its decision making "as much as any concern for Northern Ireland".
"While they seek to take the views of people in Northern Ireland on the issue of Brexit at home, their (the Irish government's) representatives are sent out around the world to talk down our economy and attempt to poach our investors," she said.
Reacting to her comments on Sunday, the Republic of Ireland's Foreign Affairs Minister Charlie Flanagan said he was "very surprised and concerned" about Mrs Foster's remarks.
The Deputy First Minister Martin McGuinness shared Mr Flanagan's sentiments in an interview with the Irish Broadcaster RTÃ‰.
Mr McGuinness told RTÃ‰ he met with a Chinese investor alongside Mrs Foster and the Chief Executive of Invest NI, but that Mrs Foster's did not mention her concerns.
He added that Northern Ireland would be "living in a fools paradise" if it did not consider that US investors would be cautious about the market as a result of Brexit uncertainty.
The first minister has said she believes technology could be used to control the border with the Republic of Ireland following Brexit.