The charges against al-Nashiri marked the last active Guantanamo military tribunal, bringing all cases into compliance with Obama's January 22 executive order to halt court proceedings at the detention centre in Cuba.
The hearing had been set for Monday.
Last year the Bush administration charged al-Nashiri with "organising and directing" the bombing and planned to seek the death penalty in the case.
"We have already waited eight years. Justice delayed is justice denied. We must allow the military commission process to go forward"
Retired Navy Cmdr Kirk S. Lippold, commanding officer of the USS Cole
Al-Nashiri said he confessed to helping plot the USS Cole
bombing only because he was tortured by US interrogators.
The CIA has admitted he was among terrorist suspects subjected to waterboarding, which simulates drowning while being interrogated in secret CIA prisons.
Obama met the families of victims of the USS Cole bombing as well as the September 11, 2001, attacks, on Friday to discuss his plans regarding Guantanamo. Some families of victims have opposed his decision.
"I was certainly disappointed with the decision to delay the military commissions process," Retired Navy Commander Kirk S. Lippold, the commanding officer of the Cole when it was bombed in Yemen in 2000, said.
"We have already waited eight years. Justice delayed is justice denied. We must allow the military commission process to go forward."