Lord Justice John Thomas and Justice David Lloyd Jones said the paragraphs, which relate to how Mohamed was treated while in custody, should not be kept secret.
"Of itself, the treatment to which Mr Mohamed was subjected could never properly be described in a democracy as 'a secret' or an 'intelligence secret' or 'a summary of classified intelligence," they said in their ruling.
Lawyers for David Miliband, Britain's foreign minister, have argued that releasing the information would harm the UK's national security and its relations with Washington.
Clare Algar, executive director of Reprieve, a UK-based legal action charity, said it was "truly bizarre" that Miliband was seeking to withold the information since much of it was already in the public domain.
"The government's obsession with secrecy is starting to feel like a hall of mirrors"
the executive director
"The government's obsession with secrecy is starting to feel like a hall of mirrors," Algar said.
"Nobody believes that disclosure will upset the US when the very same information has already been disclosed by the Obama administration."
Edward Davey, the foreign affairs spokesman for the opposition Liberal Democrat Party, said: "The government's claim that this evidence would endanger national security looks more flimsy than ever.
"David Miliband must end this shameful episode now and allow the judges to publish the redacted material from their judgment.
"It is especially galling that the foreign office has spent hundreds of thousands of pounds of taxpayers' money in an attempt to cover up the truth."
The foreign ministry is appealing against the release of the seven-paragraph summary, as well as Thursday's ruling, and the case will be heard by the Court of Appeal on 14, 15 and 16 December.