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.

As part of BBC Scotland's coverage, leader Kezia Dugdale will take part in a half-hour webcast in which she will answer your questions.
Do you want to find out what her party's long-term plans are for Holyrood's new tax powers or how Labour's approach to education differs from other parties?
This is also your opportunity to quiz her on Europe, health, policing, crime and the state of Scotland's economy.
If you have something to ask Ms Dugdale, email newsonlinescotland@bbc.co.uk
Please put "webchat questions" in the message field of your email.
You will be able to watch the one-to-one interview, hosted by BBC Scotland political editor Brian Taylor, via BBC Scotland's politics website.

The men, aged between 19 and 46, were arrested at several locations in nearby Batam island on Friday.
The plot allegedly involved firing a rocket from Batam, just south of Singapore, at Marina Bay - an upmarket, waterfront area.
Singapore officials said they were aware of the plot and security had been stepped up.
Indonesian police spokesman Boy Rafli told BBC Indonesian that the suspects were now being questioned. It is not clear whether the men had the ability to carry out such an attack.
Police said they were investigating whether the suspects had links to Indonesian militant Bahrun Naim, one of the alleged masterminds of the 2016 Jakarta attacks.
Singapore's Marina Bay is one of the country's most popular tourist destinations and the Marina Bay Sands hotel is an iconic structure on Singapore's skyline.
"What we understand so far is that they were planning to attack vital objects, busy areas including police offices," police spokesman Agus Rianto told Reuters news agency.
Singapore's Ministry of Home Affairs (MHA) said in a statement: "Our security agencies have been coordinating closely with the Indonesian authorities since the discovery of this attack plot, to monitor the activities of the group and to apprehend those involved."
The first minister has said she believes technology could be used to control the border with the Republic of Ireland following Brexit.
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The Scottish Labour Party will be holding its spring conference in Glasgow on Saturday.
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Indonesian police have arrested six people they say were planning to attack Singapore.