The postponement revived memories of disputes between the two countries that led to reductions in the supply of Russian gas to Europe through Ukraine's pipeline network in 2006 and 2009.
Viktor Yanukovich, whose country is a transit route for Russian gas, had been due to meet the Russian president in Moscow to try to secure a reduction in Ukraine's fuel bill.
But Kremlin foreign policy aide Yury Ushakov said Yanukovich had postponed the talks because more time was needed to prepare documents they had planned to sign.
"Yanukovich had planned to visit today and it has been decided to delay this visit," Ushakov said. "It is necessary to conduct additional expert work to complete all the documents which we had initially planned to sign."
Putin is due to meet European Union leaders in Brussels on Friday, and energy is likely to be high on the agenda, but a repeat of what have become known as the "New Year gas wars" is not likely.
Cuts to European gas supply transiting Ukraine during earlier disputes exacted a cost for both countries, prompting Europe to step up an energy-security agenda, including reduction of transit risk and diversification of supply away from Russia.
Russia's gas export monopoly Gazprom, an important contributor to the Russian state budget, depends on European exports for the majority of its revenues, while Ukraine depends on transit fees from Russia to fill its state coffers.
Gazprom, pressured by customers and competitors to reduce its gas prices, is likely to cut long-term contract prices to Europe next year to levels comparable to the spot market, a source at the company said.
The price of the natural gas Russia's gas export monopoly sells to Europe on long-term contracts could fall to around $370 per 1,000 cubic metres in 2013 from over $400 this year.
Little relief for Ukraine
Kyiv is struggling to afford its fuel bill to Russia under the current terms, which stem from a 2009 agreement over which Ukraine's former prime minister, Yulia Tymoshenko, was imprisoned on charges of abuse of office.
Kyiv says the price of $430 per 1,000 cubic metres it is paying this quarter is too high but has balked at demands for big concessions to Moscow to achieve a reduction.
These could include joining a customs union with Russia, Ukraine and Belarus.
Ushakov said Yanukovich would not attend a meeting this week of the customs union. Ukraine has observer status but is not a member.
"The meeting will be conducted without observers," Ushakov said.