Ms Kelly apologised but said risks were not substantial
Names, addresses and phone numbers - but no financial information - were among details on a computer hard drive which went missing in the US in May.
It belonged to a contractor working for the Driving Standards Agency, she said.
It is the second time in a month ministers have apologised for a loss of data after HM Revenue and Customs lost discs containing 25m people's details.
Ms Kelly said the details of learner drivers had been formatted specifically to meet the security requirements of the private contractor, Pearson Driving Assessments Ltd, and were not "readily usable or accessible" by third parties.
Risks 'not substantial'
She said the details were not sent in the post - but the hard drive had not been found where it had been expected to be, in a "secure facility" in Iowa.
The information commission had judged the risks presented by the loss were not "substantial" and there was no need to notify each person individually.
MISSING DRIVERS' DETAILS Name Address Phone number Fee paid Test centre Payment code E-mail where provided
Analysis: Testing times for PM 'No fraud' from lost discs
The details did not include bank account details, National Insurance numbers, driving licence numbers or dates of birth, she said.
"Nevertheless I apologise for any uncertainty or concern that these individuals may experience," Ms Kelly said.
She added the Driving Standards Agency had set up a dedicated advice line for candidates who took their driving theory test between September 2004 and April 2007.
Ms Kelly said the loss had emerged as part of a Department of Transport audit, as part of a review of data security across government departments.
'Systemic failure'
It appears a junior minister, Stephen Ladyman, was informed about the problem in June and agreed a series of procedures and wide audit with Pearson - but did not make the information public.
Details of candidates were sent electronically to Pearson Driving Assessments in Iowa. The hard drive was then sent to another state before being brought back to Iowa, where it went missing.
Ms Kelly said the Department of Transport was making changes to the way it handled data - including more electronic transfer and "secure couriers" for that information which could not be transmitted that way, as well as increased emphasis on the Data Protection Act.
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It follows the loss of personal details of more than 6,000 drivers by the Driver and Vehicle Agency in Coleraine, Northern Ireland in November.
Ms Kelly said that agency would be merged with the Driver and Vehicle Licensing Agency in Swansea to reduce the risk of it happening again.
And in October, the prime minister had to apologise for the loss of two discs containing the entire child benefit database - personal details of 25 million people including National Insurance numbers and bank accounts.
'Spy-in-the-sky'
Shadow transport secretary Theresa Villiers said it was further evidence of a lack of competence and "systemic failure" by the government in handling private data.
"Quite simply the government is failing in its duty to obey its own laws on data protection," she said.
This constant attempt to gather data, to get more data, to know more about you, to link it more together, all of that it seems to me is what comes into question
Susan Kramer
Lib Dems
Ms Villiers told Ms Kelly: "This incident and the HM Revenue and Customs disaster are another blow to your plans for an untested spy-in-the-sky national road pricing scheme."
Susan Kramer, for the Liberal Democrats described the further loss of data from another government department as "mind-bending".
She said: "Perhaps the answer is we should be holding less data on people or it should automatically be destroyed.
"I still can't get to the bottom of how old some of this data was on people who'd applied for drivers' licences.
"This constant attempt to gather data, to get more data, to know more about you, to link it more together, all of that it seems to me is what comes into question."
'Deep regret'
Pearson plc, the parent company of Pearson Driving Assessments Ltd, said: "We take great care over the quality and security of our data and we deeply regret this incident.
"There is no loss of sensitive financial data and no evidence of misuse. We have put in place additional measures to strengthen data security further."
The BBC's Justin Webb said the company had reported the missing hard drive to Iowa police, but referred to it has having been "mislaid" and said there was no evidence it had been stolen.
Ms Kelly's statement followed Chancellor Alistair Darling's presentation of an interim report by Kieran Poynter, UK chairman at PriceWaterhouseCoopers, into the loss of the two child benefit discs.
Some personal details of 3 million British learner drivers who had applied for the 'theory test' component of their Driving licence have been lost in Iowa, in the USA.

The data was lost on a hard drive that was owned by Pearson Driving Assessments Ltd, a private contractor to the UK driving standards agency.

Details were given by the UK Transport Secretary, Ruth Kelly, in the House of Commons at 1730 UTC yesterday. It is the first major loss of data in the UK since information on 25 million people was lost by HM Revenue in October.

In her statement to MPs, Ruth Kelly confirmed that no banking information was contained within the lost data, nor were individuals' dates of birth. She highlighted that security measures had been taken, and that the information that had been stored was not in a format "readily usable or accessible" by standard means.

Political figures in the UK continue to raise concerns about both the specific loss of this information, and the nature of governments ability to safely gather and maintain information. Susan Kramer, representing the Liberal Democrats stated "This constant attempt to gather data, to get more data, to know more about you, to link it more together, all of that it seems to me is what comes into question."