It will be carried out by Peter Davis, the lottery regulator, who is empowered to withdraw Camelot's licence if the operator is proved to have identified winners who requested secrecy.
The move follows the publication in the Sun newspaper of pictures of the winner's house in Blackburn and his workplace and details of his pay, family circumstances, and religion.
Camelot was accused of leaking enough facts to lead reporters to the man, although it denied the claim. On Wednesday it lost an injunction preventing the media naming him.
Yesterday Iain Sproat, the national heritage minister, said he had been assured by Mr Davis there was "no evidence" to show Camelot had leaked details. But he said: "We ought to protect anonimity rigorously and, clearly, it has not worked this week. We must look again at how to make it work."
He added: "I understand the winner has left his house. I was told he had even left the country." Mr Sproat also highlighted the dangers of kidnapping or burglary for big winners.
Camelot had felt they could satisfy the press by giving out a general fact or two about where the winner lived, he said, to laughter from MPs. "I quickly absolve myself from such refreshing naivety on the part of those who did it, if that was the case." But he said it had been done by Camelot with the best of intentions. "There is no case, as I currently understand it, of Camelot having breached [its licence] conditions."
The press should meanwhile examine whether offering £5,000 rewards for information about lottery winners - possibly the means of identifying the Blackburn man - was the way it wanted to continue, Mr Sproat said. "I find it extremely distasteful they are being asked to snoop and spy on their neighbours."
But he rejected calls to stop the rollover of unclaimed lottery jackpots, which caused such a high win last week.
However, Mark Fisher, Labour MP for Stoke on Trent central, accused the Government of being "complacent" about the problems he said had arisen with the lottery.
Ministers had hoped for a "weekly fairy tale" with a family winner and good causes benefiting. "But the events of this week show that under certain circumstances it can turn into a weekly nightmare and there is a danger at least that this whole enterprise is beginning to crumble in the Government's hands."