In an interview with the Reuters news agency, Klitschko said that at the moment there was no need to evacuate people, but they should be prepared to do so.
“Kyiv might lose power, water, and heat supply," Klitschko said, as quoted by Reuters. "The apocalypse might happen, like in Hollywood films, when it's not possible to live in homes considering the low temperature."
He added: “But we are fighting and doing everything we can to make sure that this does not happen."
According to Klitschko, 152 Kyiv residents have been killed and 678 buildings destroyed since the beginning of Russia's invasion of Ukraine.
But the Ukrainian capital is facing new problems, he said, due to Russia deliberately targeting critical energy infrastructure as winter sets in, Reuters reported.
Kyiv's authorities are opening more heated shelters in schools, kindergartens, online store pickup points as well as housing cooperatives. At the moment, there are around 500 set up, which is far from enough to accommodate Kyiv’s 3.6 million residents, according to Reuters.
Klitschko says residents must be prepared to evacuate since it is not unusual for temperatures to drop below -15 Celsius (5 degrees Fahrenheit).
“If electricity supply continues to be absent while outside temperatures remain low, we will unfortunately be forced to drain water from buildings," Klitschko told Reuters.
“Otherwise the water can freeze and break the entire water supply network, and buildings will then be totally unfit for further use," he warned.
He urged residents to stock up on food and water, and prepare clothes and documents to have on hand in case of evacuation when the heating stops, according to Reuters.
But he said the situation remained stable for now, with the city experiencing a 20-percent energy deficit.
“Right now there is heating in Kyiv, there is electricity ... everything works, there is no need at present (for evacuation)," Klitschko said, adding that residents must, however, be ready for the worst-case scenario.
Asked about the most urgent needs for the city, the former heavyweight boxing champion listed “a new air defense system” and tens of thousands of generators and industrial fan heaters.
Thursday is day 288 of Russia’s war on Ukraine.