The ceasefire enabled a humanitarian mission to the Russian-occupied city of Oleshky and for hundreds of stranded citizens to leave.
Russia resumed attacks on Ukraine's Kherson region on Monday, after the end of a local ceasefire in the area, the longest truce in the war between the neighbours since 2022, Kyiv said.
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A rare pause in fighting, brokered by US First Lady Melania Trump, ended on Sunday after starting on Tuesday.
The ceasefire enabled a humanitarian mission to the Russian-occupied city of Oleshky and for hundreds of stranded citizens to leave.
It was the longest pause in fighting between the neighbours in the full-scale invasion, now in its fifth year, which has killed hundreds of thousands and displaced millions.
"At around 8:00 am this morning, Russian occupiers attacked a car with a drone in the Korabelny city district" of Kherson, local authorities said in a statement, adding that a 62-year-old woman and 73-year-old man were wounded and hospitalised.
Russia refused a Ukrainian offer to extend the truce, a senior Ukrainian figure told the AFP news agency on Sunday.
Kherson's regional governor Oleksandr Prokudin had warned local people to be particularly vigilant when the ceasefire ended.
Ukraine's military alleged Russia used the pause in fighting to "fortify its positions".
Russian attacks also killed one person in Izium, a city in the country's north-eastern Kharkiv region, the local governor there said.
US-mediated talks between Russia and Ukraine are set to resume this month.
The Kremlin has repeatedly rejected calls for a wider ceasefire and said it intends to press on with its full-scale offensive to seize the rest of eastern Ukraine.
App hack
The fresh wave of strikes on Kherson come a day after Ukraine said its air raid alert system had been compromised, after baseless alerts of a radiation threat appeared on the app.
"Hi! A nuclear alert is about to go off all across Ukraine! Don't worry, the Oreshnik is on its way," one of the fake warnings in Russian said.
Several regional governors also warned that the system had been hacked and advised residents that there was no imminent threat.
By midnight local time the national alert system was operating normally, the State Emergency Service said in a statement.
"We once again urge citizens not to click on links from unknown sources and not to spread unverified information," the agency said.
And hours later, Russia also announced its emergency warnings app came under a "massive cyberattack" on Monday, in an apparent exchange of blows as their longest truce came to an end.
Moscow's emergencies ministry said hackers posted "false information" on the app, which is designed to warn the public of incoming drone attacks and other threats.