Jason Rezaian and his wife Yeganeh Salehi, also a journalist, were arrested in July. Salehi was freed on bail in October.
The Post said hopes for Rezaian's release rose in late October when a senior Iranian official said possible charges under review by the judiciary might be thrown out.
But last week Rezaian was shown a document signed by the judge overseeing his case and authorizing the extension of his detention, the family said.
The document was dated November 18 and said the investigation against Rezaian continued, the Post said.
Rezaian holds dual US-Iranian citizenship. But Iran does not recognize the reporter's American citizenship, the Post said.
It remains unclear why Rezaian, 38, and Salehi were arrested on July 22 or what charges they are facing. One conservative newspaper in Tehran has accused Rezaian of espionage.
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A lawyer hired by Rezaian's family has not been allowed to meet with him, the Post said.
"If authorities had evidence that Rezaian had committed a real crime, they should have charged him shortly after his arrest," said Sarah Leah Whitson, Middle East and North Africa director at Human Rights Watch.
"At this point, they should simply release him," she added.
The Post said that Ali Rezaian, Jason Rezaian’s brother, said in an interview "there seems to be a disconnect" between elements of the Iranian government.
His brother has now been held longer than any other accredited Western journalist in the past, Rezaian said. "There have not been any charges against him, and there is no reason to think he is guilty of anything."
"We have never had a clear view of why Jason is being held, how long he would be held, what might lead to his release, or when. We still don’t," said Post Executive Editor Martin Baron.
"The key thing to remember is that he should never have been arrested and imprisoned in the first place, and he should be released immediately. There was no legitimate reason for him to be held without charges or explanation for more than four months. We again urge the Iranian authorities to give him his freedom and allow him to reunite with his family."