It is the first in a series of delays sought by Obama as his administration reviews the legal system for prosecuting alleged terrorists.
Army Col. Patrick Parrish, the judge in the case, issued a written order granting the 120-day suspension without a hearing.
Later, a judge is to consider suspending the case of five men charged in the Sept. 11 attacks.
In the motion filed for the Sept. 11 case, U.S. military prosecutor Clay Trivett said a continuance is necessary in all pending cases because the review may result in significant changes to the system.
"The interests of justice served by granting the requested continuance outweigh the interests of both the public and the accused in a prompt trial," Trivett wrote. He said the motion was written at the direction of the president and defense secretary.
"It will permit the newly inaugurated president and his administration to undertake a thorough review of both the pending cases and the military commissions process generally," he added.
Human rights groups at Guantanamo to observe this week's session of the war crimes court welcomed what appeared to be the looming end of the special tribunals.
"It's a great first step but it is only a first step," said Gabor Rona, international director of Human Rights First. "The suspension of military commissions so soon after President Obama took office is an indication of the sense of urgency he feels about reversing the destructive course that the previous administration was taking in fighting terrorism."
Mr. Obama has said he will close Guantanamo, where the U.S. holds about 245 men, and had been expected to suspend the widely criticized war-crimes trials created by former President George Bush and Congress in 2006.
The president's nominee for attorney general has said the so-called military commissions lack sufficient legal protections for defendants and that they could be tried in the United States.
But CBS News foreign affairs analyst Pamela Falk says the new American leader faces a significant challenge in closing the prison camp. Mr. Obama needs to figure out what to do with the detainees already cleared for release, the detainees deemed low-level criminal suspects, and the handful of high-value detainees implicated directly in the Sept. 11 terror attacks.
"The Obama Administration needs time to formulate a detailed plan for closing the base and to negotiate with foreign leaders to accept detainees who cannot return to their home countries," said Falk, "and freezing the military tribunals gives it time to do that, while making sure no more harm is done."
Jamil Dakwar, director of the human rights program at the American Civil Liberties Union, said it was a positive step but "the president's order leaves open the option of this discredited system remaining in existence."
Relatives of victims of the Sept. 11 attacks, who were also at the base to observe the hearings, have said they oppose any further delay in the trials of the men charged in the case.
The motion for a suspension came on the day a military judge adjourned the war crimes court just before Mr. Obama was sworn in by noting the future of the commissions is in doubt. The hearings were dismissed until Wednesday "unless otherwise ordered."
There are war crimes charges pending against 21 men, including the five charged with murder and other crimes in the Sept. 11 case. Judges will be required to suspend the other cases as well though hearings may not be necessary.