In a post on Telegram, the city’s mayor Vadim Kstenin, said windows in a number of buildings had been blown out and people from one residential block had been evacuated.
He added: “There were no fires or other serious consequences.”
Kstenin said the state of emergency would allow for “prompt implementation of measures to replace” broken windows, adding: “Citizens will also be compensated for damage caused to property.”
Russia’s defense ministry said five Ukrainian drones had been destroyed and three others intercepted overnight in the Voronezh region, which borders Ukraine.
Images distributed by the Voronezh governor Alexander Gusev showed a blackened residential building, where the child was injured by fragments of a drone that was shot down, AFP reports.
"The girl, born in 2013, suffered cut wounds to her arm, leg and neck. Medical assistance was provided at the scene," he said in a statement.
Kyiv has not yet commented on the alleged attack.
The Voronezh region has been the site of several attacks in recent weeks though not all have been by Ukrainian forces.
Earlier this month, a Russian jet accidentally dropped its payload on the village of Petropavlovsk in the region, damaging several private homes.
Moscow’s military confirmed that six private residences had been hit but said that there were no injuries.
Last month, pro-Ukrainian volunteers associated with the Freedom of Russia Legion (LSR) claimed responsibility for an explosion at an oil depot in Voronezh.
Commenting on the attack, the LSR said: “To destroy the enemy’s fuel on the front, you need to conduct reconnaissance, spend an infinite number of shells, involve gunners and UAV operators.
“To destroy the fuel in the rear, you need a matchstick and one sleepless night.”
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