Mayor Vitaliy Klitschko warned that the temperature in homes could drop rapidly in the event of "a blackout and the destruction of infrastructure and a total absence of electricity, water supply, drainage and heat supply".
"The temperature in the apartments may not differ much from the outside temperature," the former boxing champion told a security forum in Kyiv, where temperatures are around -4 degrees Celsius (25 degrees Fahrenheit).
"I appeal to the people ... to have a supply of technical water, drinking water, durable food products, warm clothing."
The war has entered a relentless new phase with the onset of the first winter since Russia's Feb. 24 invasion of Ukraine.
Klitschko also said that if there were no heat or water for between 12 and 14 hours at a temperature of -5 Celsius, the city would have to drain water from residential heating systems to prevent permanent damage.
"We would not be able to restore this system till spring and it would be a big challenge," he said.
Power units at several power stations across Ukraine had to conduct emergency shutdowns this week after a spate of Russian missile strikes.
Klitschko said people should consider temporarily moving to stay with friends or relatives who own houses on the outskirts of Kyiv.
On Tuesday, Prime Minister Denys Shmyhal said Ukraine still had a 30% deficit of electricity, six days after the last big wave of Russian missile strikes on its power grid.
To remedy the lack of heating and electricity, Kyiv authorities set up 430 heating points where people can warm up and recharge their phones, but Klitschko said that the number was insufficient for a city of 3.5 million people.
"Not even 500 would help, even 5,000 would be too little."
Russia says its attacks on vital infrastructure are militarily legitimate, and that Kyiv can end the suffering of its people if it yields to Russian demands, which Moscow has not spelled out. Ukraine says attacks intended to cause civilian misery are a war crime.