The attacks were carried out less than an hour after the Israeli military issued an evacuation order for several buildings in the densely populated suburb.
In a post published on X, the Israeli military's spokesperson Avichay Adraee urged concerned Lebanese citizens to "urgently" evacuate.
The area of al-Dahiya is known as one of the strongest strongholds of the Shia militia Hezbollah.
Four people, including a mayor, are reported to have been killed in an Israeli attack on a residential building in the town of Baaloul in the Bekaa Valley in eastern Lebanon, according to the state-run Lebanese news agency NNA.
The mayor who was killed was active in the nearby town of Sohmor.
On Saturday morning, drones were fired from Lebanon towards Benjamin Netanyahu's residence. A few hours after the attack, the Israeli Prime Minister claimed that "nothing will deter us".
We will continue until we win, he said in a video recording, according to the newspaper Haaretz.
On Saturday, repeated rocket alerts have sounded in several locations in northern Israel.
Two people are also reported to have been killed in an Israeli attack on a car in Jounieh, north of Lebanon's capital Beirut.
