Moddon, 54, was scheduled to receive a lethal injection at 6 p.m. CDT for the July 29, 1984, murder of 27-year-old Deborah Davenport during the robbery of a convenience store in Lufkin, Texas.
The Supreme Court stopped the execution to allow enough time to decide whether to hear arguments by Moddon's attorneys that he is mentally retarded and his condition was not fully considered at his trial.
In recent weeks, the Supreme Court has stayed three Texas executions involving claims that the killer was mentally retarded. The court is expected to rule soon in a major case from Virginia involving the execution of the mentally retarded.
In Tuesday's order, the court offered no explanation for the action but noted that Chief Justice William Rehnquist, Justice Antonin Scalia, and Justice Clarence Thomas would have denied the application for the stay.
Moddon's IQ has been tested as low as 64, according to his attorney, but the prosecutor in the case told the Lufkin Daily News he had seen a state record which said he tested as high 85, which he said is more in the "average" range.
In the 1984 holdup, Moddon struck Davenport in the face after she offered him a free cup of coffee and then knocked her into a storeroom, where he repeatedly stabbed her, according to court records. An autopsy determined she was stabbed 18 times.