The Home Office sent about 100 letters “in error” to EU citizens living in the UK, telling them they had to leave or be liable for “detention”.
The mistake emerged after a Finnish academic, who has the right to live in the UK, received one of the letters.
Dr Eva Johanna Holmberg, who is married to a British citizen, said she “couldn’t believe my eyes” when it told her she had a month to get out.
The Home Office said the rights of EU nationals in the UK “remain unchanged”.
Prime Minister Theresa May called it an “unfortunate mistake”.
Dr Holmberg, who works at London’s Queen Mary University, had originally applied for a “qualified person certificate” before receiving the letter.
These certificates – for citizens from the European Economic Area or Swiss nationals – confirm the right to live in the UK for those who meet certain criteria.
The historian said the “absurd nonsense” had made her “even less likely” to trust politicians in the wake of Brexit.
“When I opened this, I could not believe my eyes seeing words like ‘a decision has been taken to remove you from the United Kingdom’,” she told the BBC.
The letter said she was facing detention unless she left the UK with one month, she added.
The academic spent the next few days contacting a lawyer, her employer, and attempting to speak to the Home Office.
On Wednesday, the Home Office contacted her personally to apologise – six days after she first opened the letter.
She said a “Twitter storm” had been created after her story first emerged in a newspaper in Finland.
“I have been in contact with numerous people on Twitter, on email and on Facebook,” she said. “I am yet to go through all of those messages but I have seen other people reporting similar experiences.”
Prof Simon Gaskell, Principal of Queen Mary University, said it is vital the UK government makes clear it understands “the huge contribution” overseas academics make.
“Dr Holmberg and her family should not have been subject to such stress, and it should not have been necessary for support mechanisms at Queen Mary University of London to be activated,” he said.
The Home Office said everyone who received a letter would be contacted to “clarify that they can disregard it”.
“A limited number of letters were issued in error and we have been urgently looking into why this happened,” a spokesperson added.
The prime minister said the Home Office had “moved quickly to contact all the people who had received these letters and to reassure them that they were not going to be deported”.
“I want to reassure all EU nationals here in the United Kingdom that their rights and status here in the UK has not changed,” Mrs May told the BBC.
However, critics have raised concern for the 3.2 million EU citizens living in Britain after the UK leaves the EU.
James McGrory, executive director of the pro-EU group Open Britain, said: “This is shameful stuff from the same department that gave us the disgraceful ‘go home’ vans a few years ago.
“It’s little wonder that many EU citizens feel worried about their future status in the UK when they hear of people with every right to be here getting letters threatening their deportation.”
Caroline Lucas, co-leader of the Green Party and Dr Holmberg’s constituency MP, said the case “beggars belief”.
“Mistakes like this are simply not good enough. The government is turning lives upside down by callously playing hard ball over Brexit and it needs to take its responsibilities far more seriously,” she added.
Lib Dem home affairs spokesman Ed Davey said the letters were “appalling” and “shame Britain”.
He called for Home Secretary Amber Rudd to personally apologise to those affected and to ensure they are reimbursed for any legal costs incurred because of the letters.