The 10th Circuit Court of Appeals granted the stay so it could consider a defense request for a change of venue in the trial of Brian David Mitchell, a homeless self-styled preacher who is accused of kidnapping and sexually abusing Smart in 2002.
The stay caused U.S. District Judge Dale Kimball to suspend opening statements in the Salt Lake City courtroom.
"I am of course very unhappy with this," Kimball told the courtroom. "I have to do what the 10th circuit says. I don't know what they'll do when they consider it, but for today we're in recess for this matter."
Mitchell's lawyers have said the sensational nature of the case requires that it be moved out of Smart's hometown.
Mitchell is accused of kidnapping Smart, who was then 14, from her home in 2002 and holding her captive for nine months.
Smart was rescued after she was spotted living on the streets of Sandy, Utah, with Mitchell and another woman. Prosecutors say they believe Mitchell was obsessed with making Smart a plural wife.