The tapes are believed to have shown harsh interrogation tactics used by CIA officers questioning Abu Zubaydah and Abd al-Rahim al-Nashiri, both al-Qaeda suspects, in 2002.
The US justice department and Congress are now investigating the tapes' destruction.
" It was only a matter of time before a court ordered the government to account for its handling - or mishandling - of evidence in these cases"
David Remes, lawyer
At the time of the tapes' destruction, the government was under court orders to retain evidence relevant to terror suspects at the US detention centre at Guantanamo Bay, Cuba.
After the destruction of the tapes became public in December, lawyers for several detainees went to court demanding to know more.
"There's enough there that it's worth asking ... [why the videos or other documents were destroyed]," Charles Carpenter, a lawyer said.
"I don't know the answer to that question, but the government does know the answer and now they have to tell judge Roberts."
A federal judge in New York said earlier this month that destroying the tapes appeared to have violated his order in a case involving the American Civil Liberties Union.
But US district judge Alvin Hellerstein has not yet said how he will rule.
Roberts issued a three-page ruling late on Thursday siding with Carpenter, who represents Guantanamo Bay detainee Hani Abdullah.
The judge said the lawyers had made a preliminary showing that information obtained from Abu Zubaydah was relevant to the detainee's lawsuit and should not have been destroyed.
Roberts said he wants a report by February 14 explaining what the government has done to preserve evidence since his July 2005 court order, what it is doing now and whether any other potentially relevant evidence has been destroyed.
Dean Boyd, US justice department spokesman, gave no comment.
David Remes, a lawyer in a similar case who unsuccessfully sought information about the videotapes, praised the ruling.
"It was only a matter of time before a court ordered the government to account for its handling - or mishandling - of evidence in these cases," Remes said.