A US District Court judge, Colleen Kollar-Kotelly, granted a stay in the military trial, which was due to begin on Friday at the US military base at Guantanamo Bay in Cuba.
Hicks's lawyers had asked Judge Kollar-Kotelly to grant the stay.
She ordered Hicks's military commission trial to not proceed
until the case of another Guantanamo Bay inmate, Yemeni national Salim Hamdan, is finalised in the US Supreme Court.
The outcome of the Hamdan Supreme Court case will have a crucial impact on all Guantanamo inmates.
Hamdan, who is accused of being al-Qaeda leader Osama bin Laden's driver and bodyguard, has challenged the legality of the military commission process, arguing US President George W Bush did not have the war powers to create the commissions and that they violate international law.
Hicks has also challenged the military commission process in the US District Court before Judge Kollar-Kotelly, but Hamdan's case is the first to make it to the Supreme Court, the highest court in the US.
Judge Kollar-Kotelly, in her ruling, said the stay in Hicks's case would be granted "pending the issuance of a final and ultimate decision by the Supreme Court" in the Hamdan case.