The Information Commissioner's Office (ICO) said the Better Together campaign fronted by former Labour Chancellor Alistair Darling failed to register to process personal data.
However, Better Together, launched in June by Mr Darling, said it understood the registration had been completed.
A spokesman said: "We will be contacting the Information Commissioner as a matter of urgency to discuss why there appears to be this issue.
"We would like to assure everyone who has registered their support with us that their information has been handled in strict accordance with the law."
The UK's independent authority on information rights said Better Together only requested notification forms on July 30. It said failure to notify was a criminal offence.
A spokesman said: "They were sent out a pack. They need to fill in those forms and get them back to us as soon as possible."
Angus Robertson, the SNP's referendum campaign co-ordinator, said: "This is a serious blow to the credibility of the No campaign, from which it will struggle to recover.
"We now know that – whether due to staggering complacency or incompetence – it has been engaged in illegal activity since its launch.
"As a director of Better Together, Alistair Darling along with its other board members bears personal responsibility for the No campaign's failure to comply with data protection law – an extraordinary position for the former Chancellor to find himself in.
"If Better Together cannot run a campaign without breaking the law, why on earth should anyone take them seriously on the issue of Scotland's constitutional future?"
The news came as a poll found a quarter of Scots teenagers who may be able to vote in the independence referendum favour separation.
Almost 2500 people who will be at least 16 by 2014, were questioned about their voting intentions.
Some 59% of fourth-year pupils at 24 schools north of the Border were opposed to independence, 26% backed it and 15% were unsure.
The Scottish Government proposes extending the vote to 16 and 17-year-olds.
A total of 2457 pupils at both state and private schools took part in the survey, which found 66% support for the lowering of the voting age to 16 for the poll.
An SNP spokeswoman said the party was pleased to see young people engaging in political debate, and added: "That's precisely why the SNP believes that 16 and 17-year-olds deserve to be allowed to vote in elections."
Labour MSP Patricia Ferguson said young people were turning their back on independence.
"Young people want the Scottish Government to focus on tackling the record levels of youth unemployment and turning round our economy," she said.
"Instead, Alex Salmond and his Government are obsessed with the constitution."
Conservative constitution spokesman David McLetchie said: "We regularly hear from the SNP about how young people are minded towards independence.
"But the results of this poll show the reverse, with the 26% score actually being much lower than the usual 30% we see for all age groups."
Meanwhile, Scottish Secretary Michael Moore said he is confident continuing talks today about the referendum question with Nicola Sturgeon in Edinburgh will help lead to a deal.
l The Royal Society of Edinburgh and the British Academy Policy Centre have released a report outlining Scotland's past, present and future relationship with the rest of the UK, which it says is the biggest single constitutional issue facing the UK.
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