The daily said it had "credible reports" of the detention, saying it was unclear who detained them or why.
"We are deeply troubled by this news and are concerned for the welfare of Jason, (his wife) Yeganeh (Salehi) and two others said to have been detained with them," Post foreign editor Douglas Jehl was quoted in the daily as saying.
Rezaian, 38, has been the Post correspondent in Tehran since 2012. He holds both American and Iranian citizenship, according to the Post.
The detentions would be the latest of US citizens amid frictions between the two countries.
Iran and the United States broke off diplomatic relations in the aftermath of the 1979 Islamic revolution but have held increasingly frequent talks as they work on an agreement to address international concerns over the clerical regime's nuclear program.
The New York-based Committee to Protect Journalists said it was "alarmed" by the news about the Post reporter, saying it was the latest in a series of journalist detentions in Iran.
"Iran has a dismal record with regard to its treatment of imprisoned journalists. We hold the Iranian government responsible for the safety of these four."
According to the press freedom group, Iran and China are the leading jailers of journalists in the world.
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