Four people were also injured in the attack on the border village of Arkhangelskoye, Gladkov said on Telegram.
"An 11-year-old girl has been taken to hospital and the child's mother has had both feet amputated," Gladkov wrote.
The Belgorod region has come under frequent cross-border shelling and drone attacks in the course of the war.
It is adjacent to the Kursk region where Ukrainian forces pierced Russia's western border last month in an incursion that Russian forces are still fighting to repel.
Meanwhile, a Russian missile strike on Ukraine's southeastern city of Zaporizhzhia hit critical infrastructure and injured at least two people after attacks on the city late on Sunday wounded 21, regional authorities said.
One of two Russian strikes on Monday evening hit an unidentified facility and another landed in an open area, the regional governor Ivan Fedorov said on Telegram.
Ukraine's air force had issued a missile threat warning across southern regions.
Russia denies targeting civilians but thousands have been killed and injured since the Kremlin launched a full-scale invasion of Ukraine in February 2022.
Ukraine's emergency services posted a video on its Facebook page showing rescuers trying to remove debris and unblock an entry to an apartment and attending to wounded people at night in front of a damaged residential building.
I met with — Volodymyr Zelenskyy / Володимир Зеленський (@ZelenskyyUa) @Bundeskanzler Olaf Scholz. We discuss how to bring a just peace closer. The key to achieving this is to stay united. That is exactly what our Peace Formula was created for, and we have already held a successful first Peace Summit.Now we are preparing for the second… pic.twitter.com/sj4DqsEI4uSeptember 23, 2024
German Chancellor Olaf Scholz said on Monday he will not loosen rules for the use of German weapons in Ukraine's defensive fight against Russia.
The government had made "a few decisions" regarding military support for Ukraine "that are very clear to me," Scholz said in New York, just before he met Ukrainian President Volodymyr Zelenskiy.
He specified that this included restrictions that prevent Ukraine from firing missiles deep into Russian territory.
"That is not compatible with my personal stance ... We will not do that. And we have good reasons for it," said Scholz, who is in the United States for the high-level week of the United Nations General Assembly.
Zelenskiy has been persistent in his appeals to allies to allow Ukraine to use long-range missiles to hit targets far beyond the war's front line, including Russian logistics hubs and military bases.
The most far-reaching weapon delivered by Germany is the MARS II rocket launcher, which can hit targets 84km away.
Germany has permitted Ukraine to use the rocket launcher for a limited area of Russian territory near the embattled Ukrainian border city of Kharkiv.
The powerful Panzerhaubitze 2000 howitzer, which has a range of 56km, can also be deployed to defend Kharkiv.
Scholz has repeatedly ruled out the delivery of long-range precision weapons to Ukraine, regardless of decisions taken by fellow NATO allies.
He refuses to deliver Germany's Taurus cruise missiles, which have a range of about 500km, arguing that it "would bring a great risk of escalation".
A majority of Germans also oppose sending the missiles, surveys have indicated.
The United States, United Kingdom and France have delivered cruise missiles with ranges up to 300km to Ukraine.
A discussion is ongoing in those countries about whether the use of these weapons against targets on Russian territory should be generally permitted.
It is expected that Zelenskiy will discuss this issue with US President Joe Biden during his visit to Washington DC this week.
Russian President Vladimir Putin has said he would consider the use of long-range precision weapons from NATO countries against targets deep within Russian territory as the military bloc's direct entry into the war.
with DPA
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