Firms may have to do "rigorous" checks on EU staff if there is a no-deal Brexit, a minister has suggested.
Caroline Nokes said employers wouldn't be able to tell the difference between people who had settled in the UK and those who had just arrived.
In a fractious session, she was repeatedly asked by the Home Affairs Committee what the checks would be and what it would mean for those involved.
She offered to clear up any confusion in a letter to the committee.
Ms Nokes also revealed the system for EU citizens to register for settled status still didn't work on Apple phones.
The US tech giant "won't release the upgrade we need in order for it to function", she told MPs.
The government wants the estimated 3.5 million EU citizens in the UK to apply for settled status so they can continue living and working here.
This status will give EU nationals and their families who have spent five years in the UK the same rights as British citizens, including benefits, education, pensions and healthcare.
But it will not have happened by the time Britain leaves the EU on 29 March.
In fact, Ms Nokes revealed to the Commons Home Affairs committee, just 650 people had registered so far in a pilot programme.
The government insists EU free movement will end in March, but in practice, EU nationals will still be able to come and work in the UK, until the end of the planned 21-month transition period.
The only difference is that they will have to register with the authorities.
But Ms Nokes suggested that in the event of a no-deal Brexit, where there would not be a transition period, new immigration controls - including employer checks of immigration status - will apply to EU citizens next year.
"If somebody has been through the settled status scheme they would be able to evidence that," she said.
"If somebody hasn't been here prior to the end of March next year, employers will have to make sure they go through adequately rigorous checks to evidence somebody's right to work."
'More questions than answers'
BBC home affairs correspondent Dominic Casciani
The message that many MPs took away from today's Brexit evidence session was that the Home Office either could not, or would not, explain how crashing out of the EU could affect the lives of millions of people and affect the country's ability to protect the borders.
At one point the minister appeared to be unveiling a new employment-checks policy. As Caroline Nokes left the committee room, critics were already pointing out that the Home Office has no plan in place that matches what she told the committee. And with five months to go, there was still no hint of when the department would unveil its new immigration system.
On security, there were also more questions than answers. Officials revealed there had been no assessment of the damage that would be done if the UK lost access to an EU intelligence database that police officers use 1.4 million times a day to check for information gathered by their counterparts.
That scenario - and others including the loss of the European Arrest Warrant - is causing such alarm among police chiefs, they've put 500 officers on standby to manage the fall-out from a No-Deal crisis.
Ms Nokes said the government did not want to "discriminate" against EU citizens who had "every right" to be in the UK and were "welcome" to stay compared with those who were not.
"It would pose a challenge to government and indeed employers in differentiating between those two groups of people," she added.
In a statement issued later, the Home Office said: "We will protect EU citizens' rights when we leave the EU, in both a deal or no-deal scenario.
"We are considering a number of options for the unlikely event that we reach March 2019 without a deal, and will set out more information shortly."
'Cloud of uncertainty'
But Lib Dem Home Affairs spokesman Sir Ed Davey warned of a repeat of the Windrush scandal, which saw people with the right to live in the UK threatened with deportation because they did not have the right paperwork.
"Millions of EU citizens in the UK have been living under a cloud of uncertainty for more than two years. Far from clearing up that uncertainty today, the immigration minister made it worse," said Sir Ed.
"We've already seen in the Windrush scandal how the Conservatives' hostile environment checks can destroy the lives of people who have every right to be in the UK. The government's chaotic approach to Brexit risks a repeat of that scandal for EU citizens."
In her evidence to the committee, Ms Nokes confirmed that EU nationals would not be issued with paperwork proving their immigration status.
Satbir Singh, chief executive of the Joint Council for the Welfare of Immigrants, said: "Caroline Nokes has stated that employers should check EU nationals' 'paperwork' to determine their right to work post-Brexit, despite the fact that no such paperwork exists.
"Another day, another example of a government with neither the intent nor the ability to run a fair and humane immigration system after Brexit."
Ms Nokes told the committee the government was still trying to get problems with its online application system - first identified in June - fixed.
She said it was unfair to "blame that on the Home Office" because Apple would not release an update to fix the "chip checker".
Applicants for settled status with Android phones will be able to download an app which can read the chip in their passport to verify their identity - and they will be able to take a "selfie" that can be checked against Home Office records.
But Apple device users will not be able to make use of this app, and instead will have to send in their passport to prove their identity.