Ukrainian Foreign Ministry spokesman Oleg Nikolenko said the incursion occurred during air strikes on the port of Izmail.
“According to Ukraine's state border guard service, last night, during a massive Russian attack near the port of Izmail, Russian 'Shaheds' fell and detonated on the territory of Romania,” he wrote.
“This is yet another confirmation that Russia's missile terror poses a huge threat not only to Ukraine's security, but also to the security of neighbouring countries, including Nato member states.”
Mr Nikolenko published an image showing the flames of an explosion on the opposite bank of the Danube River, the dividing line between Ukraine's Odesa region and Romanian territory.
A spokesman for Ukraine's State Border Guard Service said Mr Nikolenko's account was “reliable” and that two detonations had been observed.
However, the Romanian Defence Ministry “categorically” denied the Ukrainian assertion.
“At no time did the means of attack used by the Russian Federation pose a direct military threat to Romania's national territory or territorial waters,” the ministry said.
Romania belongs to Nato, which has a collective defence commitment that considers an attack on one ally to be an attack on all of its members.
Ukrainian President Volodymyr Zelenskyy's chief of staff Andriy Yermak said the incident showed the need to increase supplies of modern air defence and long-range weapons to deprive Russia of the ability to launch drones and missiles.
“Additional weapons and long-range missiles for Ukraine [are needed] to speed up the de-occupation of our territories. Russia must be defeated on the battlefield,” Mr Yermak wrote on the Telegram messaging app.
Ukraine's Danube ports, Reni and Izmail, accounted for about a quarter of grain exports before Russia pulled out of a UN-backed deal that provided safe passage through the Black Sea.
The Danube ports have since become the main route out of Ukraine, with grain also sent on barges to Romania's Black Sea port of Constanta for onward shipment.
The overnight attack on Ukrainian port infrastructure took place hours before scheduled talks between Russian President Vladimir Putin and Turkish President Recep Tayyip Erdogan.
While most fighting during Russia's invasion has taken place within Ukraine's borders, Kyiv has occasionally claimed the conflict has spilt over into European countries, claims that its Nato allies have largely dismissed.
In March 2022 a Soviet-made Tupolev drone crashed into the Croatian capital Zagreb causing no injuries, and in November a missile landed on a Polish village near the Ukrainian border, killing two.
Ukraine said Russia was behind both incidents but in both case its western allies dismissed this, suggesting instead that they were of Ukrainian origin and had fallen accidentally.