Earlier on Wednesday, the trial of Omar Khadr, a Canadian detainee, was also suspended for 120 days.
Khadr, who was arrested in Afghanistan at the age of 15, is accused of killing a US soldier with a grenade in Afghanistan in 2002 and has been held for seven years.
"The practical effect of today's ruling is to pronounce the military commissions process dead"
Omar Khadr's defence lawyer
Navy Lieutenant Commander William Kuebler, Khadr's defence lawyer, said: "The practical effect of today's ruling is to pronounce the military commissions process dead."
Other judges trying Guantanamo cases are expected to rule on the presidential call.
Obama's request was among his first actions as president, after being inaugurated on Tuesday.
The delays will give the Obama administration time to review the legal system for prosecuting suspects held at Guantanamo Bay.
Prior to his inauguration, Obama said he would close down the Guantanamo Bay detention centre.
Jamil Dakwar, the director of the human rights programme at the American Civil Liberties Union, said Obama's request was a positive step but "the president's order leaves open the option of this discredited system remaining in existence".
Prosecution lawyers had been seeking to halt the military tribunals pending a review by the new US administration, with the option of them being restarted at a later date.
|Human rights groups have condemned the
treatment of Guantanamo prisoners [EPA]
But defence lawyers have called for the charges to be withdrawn in a way that would allow them to be re-filed under a different legal system.
The legal manoeuvrings came after a military judge adjourned the Guantanamo Bay military court ahead of Obama's swearing-in as US president on Tuesday..
About 245 people are still held at the prison camp in Cuba.
The Bush administration had said it planned to put 80 prisoners on trial facing war crimes charges, but only three cases have been completed.
Mohammed, Ramzi Binalshibh and three others, Mustafa Ahmed al-Hawsawi, Walid bin Attash and Mohammed's nephew, Ali Abdul Aziz Ali, face 2,973 counts of murder, one for each person killed when hijackers crashed passenger jets into the World Trade Center, the Pentagon and a Pennsylvania field in 2001.