Earlier on Wednesday, the Israeli military said it had received reports that two journalists were injured as a result of its strikes.
The death of Khalil, 43, brought the death toll on Wednesday to five people.
It was the deadliest day since a 10-day ceasefire was announced on April 16 to halt hostilities between Israel and Lebanese armed group Hezbollah.
Khalil and freelance photographer Zeinab Faraj were covering developments near the town of al-Tayri when an Israeli strike hit the vehicle in front of them.
They ran into a nearby house, which was then also targeted by an Israeli strike, Lebanon's health ministry, the senior Lebanese military official and press advocates said.
Lebanese rescuers were able to retrieve Faraj, who had suffered a head wound, according to Elsy Moufarrej, who runs the Union of Journalists in Lebanon.
When rescuers returned to help Khalil, the Israeli military dropped a sound grenade, blocking their access to the damaged building, Moufarrej and the senior military official said.
Lebanese Prime Minister Nawaf Salam said the targeting of journalists and the obstruction of relief efforts constituted war crimes.
"Lebanon will spare no effort in pursuing these crimes before the relevant international bodies," he said on X.
The health ministry said Israel's military "prevented the completion of the humanitarian mission by firing a sound grenade and live ammunition at the ambulance".
Khalil's body was found after hours of searching the rubble, the senior military official said.
Her employer, the newspaper Al-Akhbar, announced her death on its website.
The Israeli military denied it prevented rescue teams from reaching the area.
Two people were killed in the first strike on the car, Lebanese state media reported.
The Israeli military said it identified two vehicles that left a military structure used by Hezbollah and crossed the "forward defence line", which refers to the delineation of the zone of southern Lebanon that Israeli troops are occupying.
It said the cars "approached the troops in a manner that posed an immediate threat to their safety" and it struck one of the vehicles and then a nearby building.
The Israeli military said it did not target journalists.
In March, an Israeli air strike killed three journalists in southern Lebanon, with the Israeli military saying it had targeted one of the reporters.
More than 2400 people have been killed in Lebanon since Israel launched an offensive in response to Hezbollah's March 2 attack, according to Lebanese authorities.
Israel has seized a belt of territory at the border, saying it aims to create a buffer zone to shield northern Israel from attacks by Hezbollah, which fired hundreds of rockets at Israel during the conflict.
