The Home Office sent about 100 letters "in error" to EU citizens living in the UK, telling them they were 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, was told she had a month to leave.
A Home Office spokesperson said "the rights of EU nationals living in the UK remain unchanged".
Everyone who received a letter would be contacted to "clarify that they can disregard it", they said.
"A limited number of letters were issued in error and we have been urgently looking into why this happened," the spokesperson added.
Dr Holmberg, who works at London's Queen Mary University, had originally applied for a "qualified person certificate" before receiving the letter.
She said the "absurd nonsense" had made her "even less likely" to trust politicians in the wake of Brexit.
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."
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