Pictures chosen by the curators included classics like Capa's images of the D-Day landings and Alfred Eisenstaedt's VJ Day shot of a sailor kissing a woman in New York's Times Square.
The six-week exhibition at the Metenkov House Museum in Yekaterinburg, a city in the Russian Urals, had been due to open yesterday.
But a day before the opening, the museum posted a message on its social networking websites, saying that the exhibition -- Triumph and tragedy: allies during World War II -- "will not happen... Due to the closing of the museum for an unknown period of time for technical reasons".
"The museum was closed by the federal agency on direct orders from Moscow," the police source told Kommersant.
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Other photographers whose work was featured in the exhibition -- prepared with assistance of the US and British consulates -- included Ansel Adams and W. Eugene Smith.
A museum source also said the authorities were behind the closure.
"The main reason is that the US president and the British prime minister are not coming to Russia" for WWII Victory Day celebrations next month, the source, who asked not to be identified, told AFP.
Russia is gearing up to mark 70 years since the Soviet victory over Nazi Germany on May 9 this year, with several heads of state planning to attend events in Moscow.
Few are expected however from Western countries.
Russia's relations with the West are currently at their lowest point since the Cold War due to the crisis in Ukraine.