The airstrikes pierced the cautious relief expressed a day earlier after Russian forces withdrew from a Black Sea island where they could have staged an assault on the city with Ukraine's biggest port.
The latest attack comes as Russia began shipping grain from occupied territory in Ukraine, according to local pro-Russian government officials. They said a vessel carrying 7,000 tons of cereal had left the port city of Berdyansk to be sent to "friendly countries".
Video of the pre-dawn attack showed the charred remains of buildings in the small town of Serhiivka, about 31 miles south-west of Odesa.
The Ukrainian president's office said three X-22 missiles fired by Russian bombers struck a block of flats and two campsites.
"A terrorist country is killing our people – in response to defeats on the battlefield, they fight civilians," Andriy Yermak, the chief of staff to Ukrainian president Mr Zelensky said.
Ukraine's presidential office said a series of Russian strikes in the 24 hours to Friday also killed civilians in eastern Ukraine – four in the north-eastern Kharkiv region and another four in Donetsk province.
Following the signing of a declaration of intent to join the EU, Mr Zelensky called for the process to be sped up, saying membership should not take years or decades. He pointed to the attack on Odesa as a reason for urgency to join the EU.
"We have to cover this path quickly," he said. "I urge all those holding government posts to see their duty, the work towards EU membership, as a front-line battle for our state, for Ukraine, for you and me.
"We have to work on preparations to join the EU with the same intensity and responsibility we put into preparing for the candidacy."
Mr Zelensky added: "We needed 115 days to receive the status of a EU candidate. Our path to a full-fledged membership mustn't take decades.
"You may be aware that some of your decisions will not be met with applause, but such decisions are necessary for Ukraine to advance on its path forward, and you must make them."
The airstrikes followed the withdrawal of Russian forces from Snake Island on Thursday, a move that was expected to potentially ease the threat to nearby Odesa, home to Ukraine's biggest port.
Meanwhile, Russian president Vladimir Putin warned political pressure from the West was pushing his country to accelerate its integration with neighbour and ally Belarus, led by dictator Alexander Lukashenko.
His comments come as Sweden and Finland are edging closer to becoming members of Nato.
Mr Putin has denied Russian forces targeted a shopping centre where Ukrainian authorities said a missile strike on Monday killed at least 19 people and injured another 62.
He claimed Thursday the target in Kremenchuk, a city in central Ukraine, was a nearby weapons depot and argued the Russian military did not take aim at places occupied by civilians.