Russia has stepped up its aerial attacks on Ukraine since Kyiv launched an unprecedented cross-border offensive into Russia's Kursk region last month.
The assault on Lviv, which is sheltering thousands displaced by over two years of war, came a day after a Russian strike on the central city of Poltava killed 53 people in one of the deadliest single strikes of the invasion.
"In total, seven people died in Lviv, including three children. The search and rescue operation is ongoing," Interior Minister Igor Klymenko wrote on Telegram.
The missile attack also wounded 40 people, damaging schools and medical facilities as well as buildings in Lviv's historic centre, according to the office of Ukraine's prosecutor general.
The western city near the Polish border is home to a UNESCO world heritage site that covers its old town and has been largely spared the intense strikes that have rocked cities further east.
At least seven "architectural objects of local importance were damaged" in Wednesday's barrage, all of which were located in Lviv's historical area and UNESCO buffer zone, regional head Maksym Kozytsky said.
The overnight attacks triggered renewed appeals from Ukraine for Western air defences, as well as long-range weapons to retaliate by striking targets deep inside Russia.
Sirens rang out over Lviv before sunrise on Wednesday, said Mayor Andriy Sadovy, who advised people to take shelter as air defences worked to down a barrage of missiles.
- 'Inhuman screams' -
"I heard terrible inhuman screams saying 'Save us,'" said Yelyzaveta, a 27-year-old resident of Lviv who rushed to shelter in her basement.
Others like Anastasia Grynko, an internally displaced person from Dnipro, did not have time to reach a shelter.
"The rocket hit our house. Everything was blown away. At the time of the explosion, I was somehow miraculously in the corridor, so I was not badly hurt," she said.
President Volodymyr Zelensky denounced what he called "Russian terrorist strikes on Ukrainian cities".
The attack on Lviv was part of a wider barrage on Ukraine, with 13 missiles and 29 drones launched at the war-torn country, the air force said.
The air force said it downed seven missiles and 22 drones.
Wreckage of a downed missile fell in the central city of Kryvyi Rig, Ukrainian emergency services said, damaging the Arena hotel and wounding five people.
"The hotel is destroyed from the first to the third floor. Thank God, everyone is alive," the city's head Oleksandr Vilkul said.
Ukrainian Prime Minister Denys Shmygal called for more air defence and for long-range weapons to strike Russia in the wake of the attack.
The weapons delivered by Ukraine's Western partners since the invasion often come with restrictions prohibiting their use against targets located inside Russia.
The overnight attack took place the day after Russia launched one of the single deadliest strikes of its two-and-a-half-year invasion in the central city of Poltava.
Fifty-three people were killed and 271 injured in an attack that hit a military educational institution -- though authorities did not say how many of the victims were military or civilians.
- Russia advances -
The Lviv attack came as Russia claimed to capture the village of Karlivka in east Ukraine, one of a string of advances in recent weeks as it seeks to capture the Kyiv-held stronghold of Pokrovsk.
Karlivka is about 30 kilometres (19 miles) from Pokrovsk, a city that lies on a key supply route for the Ukrainian army and has long been a target for Moscow.
Russian President Vladimir Putin said on Monday his army was making rapid advances in the Donbas that covers the Ukrainian regions of Donetsk and Lugansk.
"We have not had such a pace of offensive in the Donbas for a long time," he said.
Ukraine this week underwent a major reshuffle in its government, as Zelensky seeks to boost government efficiency two and a half years into Russia's invasion.
Ukraine's wartime Foreign Minister Dmytro Kuleba submitted his resignation on Wednesday, a day after six other officials including cabinet ministers said they were stepping down.
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