The Driver and Vehicle Agency in Northern Ireland has lost the personal details of 6,000 people.
The drivers' details were on two discs
The data was on two discs and went missing after being sent to the agency's headquarters in Swansea.
The DVA said the data was being provided in response to a safety recall by a number of manufacturers.
The head of the agency said the information was not encrypted. It included details of 7,685 vehicles and more than 6,000 vehicle keepers.
The data includes the keeper's name, address, registration mark of the vehicle, chassis number, make and colour.
However, the DVA said no personal financial data was on the discs.
"Letters have been sent to all registered keepers of vehicles involved," it said.
Northern Ireland's Environment Minister Arlene Foster said the discs were dispatched on 20 and 21 November and both arrived in Coventry.
However, on 5 December the DVA was told that the discs had not arrived in Swansea.
Ms Foster said she was "not optimistic" that the discs would be found.
Brendan Magee, chief executive of the Driver and Vehicle Agency, said it was "deeply disappointed" by the incident and could "understand why customers would be concerned".
He added: "We were undertaking a review of how we transmit all this information. We completed that review last week.
"Unfortunately, this incident had taken place before we completed the review and we deeply regret it and we regret the embarrassment we caused to the customers.
"It wasn't encrypted. This was one of the problems we had identified through our review, that this was an actual weakness. We are now looking at alternative methods of transporting this information."
Louise McElheron, one of those affected by the incident, said: "We have to provide our details to these government agencies to get child benefit and register cars.
It is the second major blunder involving lost government data
"We're trusting that they will treat our data with respect. And really we're victim to lax procedures, careless individuals or at worst dishonesty."
In a statement, Parcelforce Worldwide said it apologised for the loss of the two discs.
It said it had "searched exhaustively" for the packages "and will continue to work with the DVLA in our efforts to trace them".
Shadow Transport Secretary Theresa Villiers said it "beggars belief" that the government was "still losing CDs with thousands of people's personal data in the post".
"It looks like it has failed to learn anything from the HMRC catastrophe," she said.
It is the second major blunder involving lost government data in recent weeks.
Last month, two discs containing the personal details of 25 million people were lost after HM Revenue and Customs sent them unregistered and unencrypted.
Special telephone helplines have been set up for anyone concerned about the latest loss: 028 70341357 and 028 70341428.
I've been telling government organisations about exactly this type of risk for some time, as part of my job. Time and time again we are told that "after risk assessment the risk did not justify the costs of the software". Protection of sensitive information should be the priority rather than budgets. This kind of thing is bad enough once, but for it to happen again in another government body within two weeks is incredible.
G Forrester, Poole UK
Why with the technology available in this day and age are government departments still sending sensitive data around via the post? Also more worryingly, why isn't sensitive information encrypted for security? Surely information should be send via a secure network connection between offices?
Jonathan Milton, West Midlands
I'm not surprised at this recent saga involving the dvlni. I applied for a provisional licence and included my passport with the application. I never received my passport back as the dvlni say they never received it, yet I still received a licence with no identification. They do not send items by recorded delivery and the royal mail cannot trace 1st & 2nd class mail. The dvlni response is sorry and because of this I am out of pocket by £73. It's a disgrace.
tracy millar, belfast
I've said it before but as a manager in the Civil Service the main problem isn't about cuts or lack of resources. Too many Civil Service managers now spend their time managing their own careers, trying to tick boxes and telling their senior officers what they want to hear to make themselves look good. Too few now practice what they're actually paid for (ie managing staff, developing procedures, providing support, ensuring compliance and consistency and reducing bureaucracy).
Iain Scott, Newcastle
As yet I don't know if my details were among those lost. I trust the current government will abandon the idea of National ID cards with much more personal info on them. No doubt they will have "top security measures" in place to prevent id theft, except of course when they decide to post the discs with our info on them!
Eunan Jackson, Kilkeel
I do wish government departments would stop calling us "customers". Customers can take their business elsewhere: HMRC and DVLA are not operating in a competitive market environment.
Steven Baker, High Wycombe, UK
The government force us to give them our personal details under threat that if we don't we are liable for large fines or imprisonment. Yet when they loose this data they shake their heads and say oops sorry. So where are the large fines and imprisonment for them or is this yet more proof that this is not a fair or equal society?
michael atkins, waltham abbey essex
And we wonder why Identify Theft has become a problem....
Paul Simpson, Leicester