He said deliveries to Ukraine had been reduced by 40 million cubic metres a day.
Ukraine's state energy firm, Naftogas, confirmed that supplies had been reduced, but gave a different figure of 30 million cubic metres a day.
It also said the reduction was not significant and would have no impact on consumers in Ukraine.
The cutoff came just hours after Gazprom's chairman, Dmitry Medvedev, won the Russian presidential election with the support of his mentor Vladimir Putin, the current president.
Putin and Medvedev have increased the Kremlin's control over Gazprom and used it to help energy-rich Russia expand its economic and political influence abroad.
While Russia has threatened to sever supplies to Ukraine several times in recent years, the only previous time it did so was on New Year's Day 2006, when the cutoff affected some European consumers.
Much of the Russian gas consumed in Western Europe comes in pipelines that cross Ukraine.
Viktor Yushchenko, the Ukrainian president, and Putin reached an agreement last month to avert another threatened cutoff. Yushchenko insisted last week that Ukraine had paid off its debt - but Gazprom said the payments only covered 2007 supplies, not debt still outstanding from previous years.