Gazprom had warned it would cut supplies if Ukraine failed to pay $1.95bn (£1.15bn) – out of $4.5bn it says it is owed – by 06:00 GMT.
There is no confirmation supplies have been ended. The Russian firm said it would continue to supply gas to Europe.
Russia-Ukraine ties remain tense since Moscow annexed Crimea in February.
Kiev accuses Moscow of supporting separatists in the east of the country. Russia denies the charge.
EU Energy Commissioner Guenther Oettinger: “They insisted [on getting] the $1.9bn (£1.15bn) immediately”
“Today, from 10:00 Moscow time, Gazprom, according to the existing contract, moved Naftogaz to prepayment for gas supplies,” Gazprom said in a statement.
“From today, the Ukrainian company will receive Russian natural gas only in the amounts it has paid for.”
Moments later, both Gazprom and Ukraine’s state-owned Naftogaz company filed lawsuits against each other in the Stockholm arbitration institute.
Gazprom said it wanted to recover $4.5bn from Naftogaz, which is dealing with gas supplies to Ukraine. Meanwhile, Naftogaz said it was seeking to recover $6bn in “overpayment” for gas since 2010.
The move follows crisis talks between Ukraine, Russia and the European Union on the issue.
“We reached no agreement. The chances that we meet again are slim,” Gazprom spokesman Sergei Kuprianov said after the latest round of the talks ended in Kiev over the weekend.
However, EU Energy Commissioner Guenther Oettinger, who attended the talks, said he was “not pessimistic” about a deal.
He said he would continue to work for an agreement despite his compromise proposal, that Kiev pay $1bn on Monday and the rest in instalments, being rejected by Gazprom.
Ukraine’s discounted rate for gas was axed in April after Moscow accused Kiev of failing to pays its bills.
On Monday, Gazprom stressed that it would continue to supply European consumers with gas at “full volume” and that it was Ukraine’s responsibility to make sure the gas transited through the country.
However, correspondents say the EU could be affected.
About 15 per cent of the EU’s gas supply is Russian gas which is piped through Ukraine.
Earlier this month, Gazprom gave Ukraine more time to settle its gas bill after receiving a part-payment of $786m (£469m).
Ukraine said it refused to clear its debts completely in protest at Gazprom’s recent 80 per cent price increase.
Gazprom ended its discount price for Ukraine, which was negotiated by former President Viktor Yanukovych last December, in April.
Before the discount was cancelled, Ukraine’s gas bill was heavily reduced by Russia to $268 per 1,000 cubic metres.
The price is now $485.50 per 1,000 cubic metres, the highest in Europe.
Almost 15 per cent of gas used in Europe comes from Russia via Ukraine, which is why EU members are taking a particularly close interest in the stand-off, observers say.
The talks that ended on Monday had been brokered by EU representatives.