"The Israeli attack near Hariri Hospital killed four people, including a child, and injured 24," it said in a statement from Lebanon's Health Department, which added that it had caused "significant damage to the hospital".
Rafiq al-Hariri is the largest public hospital in Lebanon and took over the treatment of certain patients who had previously been evacuated from hospitals in al-Dahiya, Beirut's southern suburbs, due to intense Israeli bombing in the area.
The attacks are said to have occurred shortly after the Israeli military urged residents in several areas to evacuate.
Just two hours earlier, the Israeli military claimed that Hezbollah was hiding hundreds of millions of dollars in cash under a hospital in Haret Hreik, a neighborhood in al-Dahiya. The hospital was quickly evacuated after the accusation, an accusation that the hospital manager has since denied.
Israel has not commented on the reports.