The strike appeared to hit the car park of the Rafik Hariri University Hospital, a hospital source told Reuters news agency. The health ministry said 24 people had been injured.
It was among 13 air strikes that hit south Beirut on Monday evening. The Israeli military said it was attacking facilities linked to Hezbollah.
An Israeli spokesman had earlier warned people to move away from several locations in southern Beirut, however Rafik Hariri hospital was not among the locations mentioned.
Videos from the Dahiyeh neighbourhood in southern Beirut, where seven locations to be targeted were announced in advance, showed locals fleeing in vehicles and on foot as the strikes began hitting.
One location identified as a target by the Israeli army was roughly 400m from Beirut airport, the only international airport serving Lebanon.
Local media shared images of some windows in an airport building that were blown in the blast.
Israel has not commented since issuing the earlier evacuation warnings.
Separately, the Israeli military said earlier on Monday that it had identified a Hezbollah bunker concealed under a different hospital in southern Beirut, which has since been evacuated.
IDF Spokesman Rear Admiral Daniel Hagari said without providing evidence that the bunker under the Sahel hospital in Haret Hreik held hundreds of millions of dollars in cash and gold that was being used to fund Hezbollah's attacks on israel.
The director of Sahel hospital denied there was a bunker underneath and called on the Lebanese army to inspect the site.
Israel appears to have expanded its war against Hezbollah beyond military infrastructure and says it is targeting the group's financial networks.
On Sunday night Israel carried out air strikes targeting branches of a financial association linked with Hezbollah in the southern suburbs of Lebanon’s capital Beirut, as well as the south and east of the country.
The Israeli military said it targeted money held by Al-Qard Al-Hassan Association (AQAH). It offers financial services to civilians in areas where Hezbollah has strong support, but Israel and the US accuse it of being a cover for the Iran-backed group to fund its activities.
There was no immediate comment from AQAH or Hezbollah.
Also on Monday, US President Joe Biden’s special envoy to the Middle East arrived in Beirut to explore the possibility of a negotiated end to the war.
Amos Hochstein said the US wanted to see an end to the war in Lebanon end "as soon as possible".
He said that UN resolution 1701 - which calls for the Lebanese state to be the only armed force in southern Lebanon - was "not enough" and the US was looking into what more needed to be done.
Hezbollah fighters meanwhile continued to fire rockets into northern Israel, with the military reporting that 170 projectiles had crossed the border by late Monday evening.
Israel began an intense air campaign and ground invasion against Hezbollah after almost a year of cross-border fighting sparked by the war in Gaza, saying it wanted to ensure the safe return of tens of thousands of residents of Israeli border areas displaced by rocket attacks.
Hezbollah began firing rockets into northern Israel in support of Palestinians on 8 October 2023, the day after its ally Hamas’s deadly attack on Israel.
More than 2,400 people have been killed in Lebanon since then, including 1,800 in the past five weeks, according to the country’s health ministry. Israeli authorities say 59 people have been killed in northern Israel and the occupied Golan Heights.
BBC