The row follows Ukraine's rejection of Russian plans to more than quadruple the price of its gas.
In an attempt to break the deadlock, Russian President Vladimir Putin had offered a three-month price freeze as long as Kiev agreed to pay the increased price after that.
Russia's state-owned gas giant Gazprom later announced that the offer had been refused and said supplies would be turned off at 0700 GMT (1800 EST).
The Russian government says Ukraine has been receiving gas well below the market rate.
Ukraine says it does not object to market prices but said the exact figures would have to be negotiated.