Steve Baker admitted he should have "corrected or dismissed" the allegation made by ardent Brexiteer Jacob Rees-Mogg that Treasury officials are attempting to influence Brexit policy.
Mr Baker said on Thursday the accusation was "essentially correct".
But he told MPs the next morning: "As I explained yesterday, I considered what I understood to be the suggestion being put to me as implausible because of the long-standing and well-regarded impartiality of the civil service...
"I accept that I should have corrected or dismissed the premise of my Honourable Friend's question."
The Wycombe MP added: "I have the highest regard for our hard-working civil servants.
"I'm grateful for this early opportunity to correct the record and I apologise to the House."
He had faced mounting criticism, including from Dave Penman, general secretary of the FDA union which represents senior civil servants.
Mr Penman said on Thursday: "To stand at the despatch box and refuse to challenge a half-baked conspiracy theory about the civil service - one that is even now being disowned by its supposed source - is the height of irresponsibility from a serving minister."
Despite the gaffe, Prime Minister Theresa May ruled out sacking Mr Baker during her visit to China.
Asked by Channel 5 News if she would fire him, Mrs May said: "No. The ministerial code says that the minister should take the earliest opportunity to amend the record … and apologise to Parliament.
"What I understand the minister did was to reflect what he thought somebody else had said at a meeting.
"He has now recalled that was not right, he is going to apologise, he is going to ensure that the record in Hansard is correct.
"That's what the ministerial code asks him to do, and that is what he will be doing."
Mr Rees-Mogg had attributed the claim to Charles Grant, director of the Centre for European Reform think tank, posting in a tweet: "Even a leading Remainer thinks the Treasury is trying to hinder Brexit."
But Mr Grant hit back, saying that after the Brexit minister's "gracious" apology, Mr Rees-Mogg should do the same.
The North East Somerset MP remained unrepentant, telling an audience at the Queen Mary University's Mile End Institute: "If he says he didn't make it, he says he didn't make it. But he made a very similar claim on Twitter."
It comes as Brexit tensions ramp up ahead of talks on the proposed transition period.
Brexit Secretary David Davis is meeting the EU's chief negotiator Michel Barnier on Monday to debate divisions over freedom of movement continuing after the official divorce day - expected to be 29 March 2019.