Lviv Mayor Andriy Sadovyi said on Telegram that one person was injured.
Maxim Kozitsky, the regional governor, said a woman was also rescued from the rubble at the site, but was not hurt. Kozitsky said the warehouse was not storing military equipment.
Lviv, located near Ukraine’s border with Poland, is a key hub for western aid entering Ukraine and has been the target of prior Russian attacks.
Ukraine’s military said air defenses destroyed 27 of 30 drones that Russia used in its attacks, with intercepts happening in southern, central and western Ukraine.
The military also said it downed a Russian reconnaissance drone in the eastern part of the country.
Some information for this report came from Agence France-Presse and Reuters