Volodymyr Zelensky said he had received intelligence reports suggesting that Moscow would launch the attacks using Iranian-made Shahed drones.
It comes after Ukraine carried out a strike that it said killed hundreds of Russian troops in the Donbas region.
In a rare admission of battlefield losses, Russia said the attack killed 63 of its troops.
Speaking from Kyiv in his nightly address, Mr Zelensky said Russia planned to “exhaust” Ukraine with a prolonged wave of drone attacks.
“We must ensure – and we will do everything for this – that this goal of terrorists fails like all the others,” he said. “Now is the time when everyone involved in the protection of the sky should be especially attentive.”
Russian drone strikes on Ukraine appear to have increased in recent days, with Moscow launching attacks on cities and power stations across the country over the past three nights.
Mr Zelensky said Ukrainian air defences had already shot down over 80 Iranian-made drones in the opening days of 2023.
Russia has been targeting Ukraine’s energy infrastructure for several months, destroying power stations and plunging millions into darkness during the country’s freezing winter.
Elsewhere, Ukraine has confirmed it carried out a strike in the occupied region of Donetsk, which it earlier claimed killed 400 Russian troops.
Russian officials contested the figure, saying only 63 troops were killed. Neither claim has been verified, and access to the site is restricted.