The announcement from the Kremlin came a day after French President Francois Hollande said Syrian forces had committed a "war crime" in the battered city of Aleppo with the support of Russian air strikes.
Putin had been due in Paris on October 19 to inaugurate a spiritual centre at a new Russian Orthodox church near the Eiffel Tower, but Hollande had insisted his Russian counterpart also took part in talks with him about Syria.
The unprecedented cancellation of a visit so close to being finalised is a "serious step... reminiscent of the Cold War", said Russian foreign policy analyst Fyodor Lukyanov.
"This is part of the broader escalation in the tensions between Russia and the West, and Russia and NATO," he told AFP.
Russia has been waging a punishing aerial bombing campaign in Syria for more than a year in support of President Bashar al-Assad's forces, part of a multi-front war that has claimed some 300,000 lives and seen Moscow further estranged from the West.
The French president had admitted he was agonising over whether to meet Putin, but the Kremlin on Tuesday called off the visit.
Kremlin spokesman Dmitry Peskov said Putin was "ready to visit when it is comfortable for President Hollande", adding that Moscow would "wait for when that comfortable time comes".
Hollande responded that he was prepared to meet Putin "at any time... to further peace".
Speaking in Strasbourg, Hollande said France and Russia had had a "major disagreement" over Syria.
"It is necessary to have dialogue with Russia but it must be firm and frank," Hollande told the parliamentary assembly of the Council of Europe rights body.
Thomas Gomart, head of the French International Relations Institute (IFRI), said the optics of a Putin visit at this time would be "explosive".
He said the cancellation was the "culmination of a divergence that has been widening" for some months between France and Russia.
'Outrage' fatigue
Outspoken British Foreign Secretary Boris Johnson waded into the row, calling for anti-war campaigners to protest outside the Russian embassy in London.
Johnson said the "wells of outrage are growing exhausted" and anti-war groups were not expressing sufficient outrage at the conflict in Aleppo.
"Where is the Stop the War Coalition at the moment? Where are they?" he said during a parliamentary debate.
On Saturday, Russia blocked a draft French UN resolution calling for an end to the barrage of air strikes on the rebel-held east of Aleppo that have escalated in the last month, leaving hundreds of people dead, including dozens of children.
It was the fifth time that Russia used its veto to block UN action to end the five-year war in Syria that has sent millions fleeing and triggered the biggest migration crisis in Europe since World War II.
In the aftermath of that decision, Hollande described the bombing of Aleppo as a "war crime".
He said in a TV interview on Monday: "Those who commit these acts will have to pay for their involvement, including at the International Criminal Court."
On Tuesday, at least 12 civilians were killed in the heaviest Russian bombardment in days of Aleppo, a monitoring group said.
An AFP correspondent and the Britain-based Syrian Observatory for Human Rights reported it was the most intense bombing since the Syrian army said on October 5 it would reduce its onslaught on the northern city.
Despite cancelling his visit to Paris, Putin is still considering travelling to Berlin on October 19 for a meeting on the conflict in Ukraine, one of his aides told Itar-Tass on Monday.
German Chancellor Angela Merkel proposed the meeting along the lines of the so-called Normandy format, bringing together Germany, France, Russia and Ukraine, with the possible participation of Hollande.
But it is uncertain whether Ukrainian President Petro Poroshenko is prepared to take part.
The outbreak of the Ukraine crisis in 2014 eventually prompted France to cancel the delivery to Russia of two Mistral assault ships and repay almost 950 million euros ($1.1 billion).
The ships were subsequently sold to Egypt.
