The Israeli military did not immediately provide comment on reports that multiple people had been killed or specify the location of the strike.
The Lebanese government is no longer providing the monthly $20,000 USD needed to maintain the hospital generators.
Hezbollah has power without responsibility, operating its own mini-administration across the nation with a great degree of impunity.
Border clashes between Israel and Iran-backed Hezbollah have escalated in recent weeks since Israel went to war with Hezbollah's Palestinian ally Hamas.
"We are aware of the incident with the Reuters journalist," an army spokesman said. "It's a tragic thing."
The Lebanese army said Israeli troops had fired smoke bombs at a Lebanese patrol that was accompanying workers removing "infringements" that the army said had been set up by the Israelis.
Israeli forces fired stun grenades at Lebanese heavy machinery that crossed the border into Israel on Saturday afternoon.
Senior White House adviser Amos Hochstein said it was "natural" to look into the issue following the delineation in 2022 of the maritime border between the two countries.
Israel is attempting to reduce Hezbollah’s ability to invade, but this has infuriated Nasrallah and it is another piece of the conflict between the sides.
Lebanon hopes gas and oil discoveries will help it reverse a crippling economic crisis that has cost the local currency more than 98% of its value.