Ruhani had been due to arrive in Moscow on Monday and had been expected to announce when Iran would sign the so-called additional protocol to the nuclear Non-Proliferation Treaty (NPT).
This allows the international nuclear watchdog, the International Atomic Energy Agency (IAEA) to conduct snap inspections of nuclear installations.
“He is not coming. The trip is cancelled, at least for the time being," said an Iranian embassy official in Moscow.
The embassy declined to provide the reason for the cancellation or whether Ruhani would reschedule his trip.
On Friday, a Russian Atomic Energy Ministry official was quoted as saying that Ruhani would announce during his Russia trip the date on which his country would sign the Additional Protocol.
There was speculation in Moscow that the cancellation was due to a visit by Israeli Prime Minister Ariel Sharon, who arrived in the Russian capital on Sunday for a three-day visit.
Israeli PM Ariel Sharon is in Russia
for a three-day visit
Sharon was to meet President Vladimir Putin on Monday to try to convince Russia to drop its efforts to turn the Middle East “roadmap" into a binding UN resolution.
On Sunday, Israeli Prime Minister Ariel Sharon arrived in Russia to discuss, among other things, concerns about Russia's transfer of nuclear technology to Iran.
Sharon would also ask Putin to keep up the pressure on Tehran over its nuclear programme, said an official with the Israeli delegation.
Asked whether Ruhani's trip was cancelled because it coincided with that of Sharon, the embassy official said: "No, I can't comment on that.”
Moscow, long criticised for its nuclear ties with Iran, has been pressing ahead with plans to help Iran build its first nuclear reactor in Bushehr. It has been fiercely criticised by the United States and Israel.