The Israel Broadcasting Corporation said on its X account that the military site was severely damaged.
This happened, she said, although it assumes the site is protected from such attacks.
The Israeli media did not clarify the nature of the site, nor the nature of the fortifications on it.
Israel's military and security services are investigating the circumstances of the incident.
Last night, 20 rockets were fired from southern Lebanon into the Upper Galilee region in northern Israel.
The rockets landed near the settlements of Shomera, which borders Lebanon, according to Israeli media.
Neither Hezbollah nor any Palestinian faction has claimed responsibility for the rocket fire so far.
This is the second time during the current Gaza war that information has emerged showing rockets falling on sensitive Israeli military sites.
The American newspaper "The New York Times" revealed on Monday that a rocket likely launched by Hamas during its surprise and unprecedented attack on October 7, hit an Israeli military base, where experts believe that many nuclear-capable missiles are present.
The newspaper said it concluded this after conducting a visual analysis of the aftermath of the Oct. 7 attack.
It said the shelling hit the Sdot Micha air base in central Israel, where the rocket set fire to the base that approached stores of rockets and other sensitive weapons.
Israel does not publicly admit to possessing a nuclear arsenal, but a number of its officials have threatened to use it against the Gaza Strip.
Israeli sources, U.S. officials and satellite imagery confirm that Israel has at least a handful of nuclear weapons.
Hans Christens, director of the Nuclear Information Project for U.S. Scientists, estimated that there were likely to be 20-25 Jericho missiles capable of carrying nuclear warheads at the base.