The annual release of government papers to the archives in Kew, west London, under the 20-year rule includes a No.10 file from 2004 and 2005 on royal visits.
The version originally made available to journalists under embargo, so they could prepare stories in advance, included minutes of a meeting where officials discussed the travel plans of various royals - including the former Duke of York.
However, the minutes were subsequently redacted from the file before it was made available to the public.
The Cabinet Office, which is responsible for transferring the files to the National Archives, blamed an "administrative error" as they had never been intended for release.
"All records are managed in line with the requirements of the Public Records Act. Any release is subject to an extensive review process, including engaging expert stakeholders," a spokesman said.
However, Graham Smith, chief executive of anti-monarchy campaign group Republic, said there was no justification for withholding the documents, especially since Andrew has been stripped of his royal status amid continuing controversy over his links with the pedophile financier Jeffery Epstein.
"There should be no royal exemption at all. But this exemption surely doesn't apply to Andrew now he's no longer a royal," Smith said.
"The most likely reason for this attempt to stop disclosure is pressure from the palace. The royals have sought to keep everything under wraps when it comes to Andrew, not to protect him but to protect themselves."
Andrew has always denied any wrongdoing.
The minutes, which were seen by journalists before they were pulled from the file, would appear to be unexceptionable.
There is discussion by senior palace and Foreign Office officials about his travel plans as a UK trade envoy - which earned him the nickname "air miles Andy" - with visits to China, Russia, south-east Asia and Spain.
Officials also raised the issue of whether the Football Association would be prepared to pay for him to attend the Euro 2004 tournament in Portugal as a royal representative.
It was noted that a change to the rules for royal travel meant that his visits as a trade envoy would in future be funded by the Royal Travel Office - rather than UK Trade and Industry - which would have to find an additional STG90,000.
Elsewhere, the minutes show that a bid for Prince William to visit China was turned down, on the grounds that he should not undertake official duties until he was at least 25.
The retention of the minutes underlines the way that files relating to the British royal family are routinely withheld from release under the Public Records Act.
