Lviv Mayor Andriy Sadovyi said that five "powerful" missiles struck the city and that emergency services were responding to the blasts. He said more details would follow.
Sadovyi said seven people were killed and 12 wounded in overnight missile strikes.
Regional governor Maksym Kozystkiy said three missiles hit military infrastructure facilities and one struck a car tire replacement facility.
Lviv has been considered a safe haven as it is relatively less affected by the fighting than other parts of Ukraine.
Local authorities have also reported explosions in the Ukrainian southern region of Dnipropetrovsk.
Russian, Ukrainian videos suggest 'prisoner swap'
Two alleged British fighters captured in Ukraine appeared on Russian state TV and asked to be exchanged for pro-Moscow politician and businessman Viktor Medvedchuk, who is being held by Ukrainian authorities.
The two men spoke after being prompted by an unidentified man.
Tens of thousands of international fighters have volunteered with Ukraine's armed forces since the start of Russia's invasion.
Medvedchuk was recaptured by Ukrainian forces last week. He had been detained on suspicion of treason until February, when Ukrainian authorities said he had escaped.
Also on Monday, Ukraine's security service released a video showing Medvedchuk asking Russian President Vladimir Putin to exchange him for the evacuation of people trapped in Mariupol.
Both Russia and Ukraine have been criticized for publishing images and videos of prisoners of war as it is considered a violation of the Geneva Convention.
More than 5 million flee Ukraine: UN
More than 4.9 million citizens of Ukraine have fled the country following Russia's invasion, the UN's refugee agency (UNCHR) said.
UNHCR said nearly 215,000 nationals of other countries residing in Ukraine have also fled.
Women and children account for 90 percent of those who escaped. Nearly two-thirds of all Ukrainian children have been forced from their homes.
"Refugees from Ukraine, the vast majority women and children, face increased risks of sexual exploitation, abuse and human trafficking," UNHCR said.
UNCHR estimated that 7.1 people have been internally displaced within Ukraine.