Fifty-year-old Gary Giordano has been in jail on the Caribbean island for nearly four months while investigators gathered and evaluated evidence in the case of missing person Robyn Gardner, 35, of Frederick, Md.
In a private hearing on Friday, the judge ruled that Giordano must be freed Tuesday without any conditions.
Prosecutors have until then to appeal the decision.
Aruban authorities have said they believe Giordano was involved in the disappearance.
Giordano, 50, an employment agency owner from Gaithersburg, maintains that Gardner was swept out to sea on Aug. 2 while snorkeling. Her body has not been found, and she is presumed dead.
Prosecutor Taco Stein said he has appealed the judge's decision.
"It's a setback," he told the Associated Press. "We feel that he is still a flight risk. ... The investigation is ongoing. We need him."
Stein said prosecutors need more time to analyze information from Giordano's laptop and iPad.
He said that if Giordano is freed and leaves Aruba, they would request his extradition from the U.S. if they could find sufficient evidence to persuade a judge to order him rearrested.
"We are determined to get to the truth of this," Stein said.
Shortly before the trip to Aruba, Giordano took out a $1.5-million accidental-death insurance policy on Gardner, according to Aruban authorities. Giordano was the beneficiary of that policy. The pair arrived on the island July 31. Gardner was last seen Aug. 2, and Giordano was taken into custody three days later.
Gardner worked as a patient coordinator at a dental practice, but recently lost her job.
Gardner had an apartment in Frederick but had been living with her boyfriend, Richard Forester, in Bethesda since January.
Gardner's trip to Aruba came as a surprise to Forester, who said he thought Gardner was going to Florida to see her family.
Gardner's disappearance has drawn international attention for months, in part because of comparisons to the still-unsolved case of Natalee Holloway, an American teenager who went missing in Aruba in 2005.
The Associated Press contributed to this report.