A software "issue" meant polling cards and some postal votes were sent out to some "non eligible" voters.
They are still awaiting responses from six councils so the number could rise.
Leave campaigners Iain Duncan Smith and Bernard Jenkin have expressed "serious concerns" about the "conduct of the EU referendum and its franchise".
They have written to the prime minister complaining of "many and varied" examples of EU nationals being sent polling cards.
On Friday, the Electoral Commission confirmed the numbers affected so far, and said the software provider had since "resolved the issue".
Any postal votes wrongly issued would be cancelled and none of those affected would appear as an eligible voter on the electoral registers used at polling stations, it said.
EU citizens from non-UK countries are not entitled to vote, unless they are citizens of the Irish Republic, Cyprus or Malta.
But Mr Duncan Smith has said a Nottingham City Council officer had emailed a Vote Leave supporter to say the council was unable to check whether people put their correct nationality on an application, and had to assume the information submitted was correct.
Kingston-upon-Thames council in south-west London said a Polish citizen in the area - whose case had been highlighted by the Guido Fawkes website - was sent a polling card because he had put "British" as his nationality on the electoral register.
British, Irish and Commonwealth citizens resident in the UK and many British citizens living abroad are entitled to vote in the referendum.
You can check with your local authority's electoral services team if you are worried that you are not on the register.
If you are not on the register you have until midnight on Tuesday, 7 June to submit an application for a vote. The deadlines for applying for a postal vote at the referendum are:
In England, Scotland or Wales, you can register to vote online anytime at gov.uk/register-to-vote. If you are a British citizen living abroad, you can register to vote online in the same way.
In Northern Ireland, visit the government's Register to vote in Northern Ireland page to download a registration form. If you are an Irish citizen living abroad who was born in Northern Ireland, visit the Electoral Office for Northern Ireland website to download the correct form.

Mr Newman was detained in Melbourne on Thursday after entering Australia without a visa.
Australia had cancelled his visa while he was still in the US on the grounds that his presence in the country could incite violence.
Mr Newman has previously called for the execution of abortion doctors and said women who have abortions are murderers.
On Friday, Justice Geoffrey Nettle in Melbourne ruled that the cancellation of Mr Newman's visa was justified, reported the Australian Broadcasting Corporation.
While Mr Newman may have had a case to challenge the cancellation, he should not have boarded a plane to Australia without a visa, said the judge.
"Acting as he did means he does not come to this court with clean hands," he said.
Mr Newman, also known as Troy Newman-Mariotti, had been due to speak at events run by the group Right to Life Australia.
But he was prevented from boarding a connecting flight in the US city of Denver on Tuesday after Immigration Minister Peter Dutton cancelled his visa.
It came after it emerged he had called in a 2000 book for doctors who perform abortions to face execution .
His wife Mellissa had presented his appeal to the high court in Melbourne.
"I don't know what they're afraid of. I don't know what they think he's going to do here," she was quoted as saying earlier by ABC News.
In a posting on Facebook ahead of his arrival in Melbourne, he said the decision to revoke his visa "was based on a pile of lies, including the idea that I promote violence".
"My 25-year history of peaceful, prayerful action speaks for itself," he said.
Earlier this week, Australian Labor MP Terri Butler wrote to Australia's Mr Dutton to ask that Mr Newman's visa be denied, calling him an "anti-choice extremist".
But the website for Mr Newman's organisation, Operation Rescue, insisted that he "has never advocated violence and in fact, urges pro-life activists to work within the governmental and legal system to accomplish change".
Polling cards were wrongly sent to at least 3,462 EU citizens who are not allowed to vote in the EU referendum, the Electoral Commission has announced.
[NEXT_CONCEPT]
US anti-abortion campaigner Troy Newman is to be deported from Australia after losing a high court appeal.