Zeidan, who became premier in November 2012, was dismissed by Libya's parliament in March 2014 amid accusations that public funds had been embezzled.
He left the country soon afterwards, in defiance of a travel ban issued by the attorney general.
Zeidan had returned to Libya in early August for the first time since his dismissal and was planning a Tripoli press conference to respond to his critics, according to Karam Khaled, a friend who accompanied him.
"It was the GNA that prepared the visit, including protocol at the airport and the hotel reservation," Khaled said.
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He said an armed group's first attempt to seize Zeidan on August 12 was foiled by hotel guards.
He said the gunmen were from the GNA-linked Tripoli Revolutionary Brigade, a militia of former rebels from the NATO-backed 2011 uprising that led to the overthrow and killing of longtime dictator Moamer Kadhafi.
"Gunmen from the same group returned the next day and we were obliged to hand them Zeidan," Khaled said.
The ex-prime minister's son Zeidan Zeidan said the family had no news of his father's whereabouts.
"We have nothing so far," he said by phone from the United Arab Emirates, where he lives.
He said his father's lawyer had told him no court cases had been brought against the former premier.
"This was indeed a kidnapping and not an arrest," he said, adding that the family is worried for the health of his father, who is 67.
Since Kadhafi's fall, Libya has been plagued by security problems and political actors have been obliged to depend on rival militias that are battling for control of the North African country.