The strikes targeted a moving convoy carrying ballistic missiles to Lebanon from Syria for use by the Shiite Islamic group, Saudi-owned United Arab Emirates TV news channel al-Arabiya reported.
Saudi Arabia and the UAE are overwhelmingly Sunni Muslim.
Hezbollah is a bitter enemy of Israel that has joined the Syrian civil war on the side of the Assad regime.
The Lebanese army did not immediately confirm the late-Monday reports, saying it was investigating them. The Israeli military declined to comment.
Israel has a longstanding policy of silence on pre-emptive military strikes.
Several militants were killed in the attack, al-Arabiya said.
The Israeli airstrikes targeted a "qualitative" weapons shipment in an area of eastern Lebanon's Bekaa Valley known to house a Hezbollah post that recruits and trains fighters, Lebanon's Daily Star reported, citing a security source.
The area, near the town of Janta, is also a well-known route for arms smuggling between Lebanon and Syria, the source added.
The Britain-based Syrian Observatory for Human Rights activist group said it could not say if the airstrikes hit on the Lebanese or Syrian side of the border.
Lebanese Broadcasting Corp. said the area has several passageways between Lebanon and Syria, through which weapons and equipment pass surreptitiously.
Lebanon's state-run National News Agency said the Israeli jet fighters carried out two air attacks.
The planes launched four rockets on the Janta area in the mountains separating the remote eastern Bekaa Valley village of Nabi Sheet from the Syrian border, the Daily Star said.
Hezbollah satellite TV station al-Manar reported "no raid" but said "enemy planes" had a "strong presence" in the north of Bekaa.
Witnesses cited by the Daily Star said plumes of smoke rose from the airstrike area. The planes then left toward the Mediterranean Sea on their way back to Israel, the Daily Star's security source said.
Israel and Hezbollah fought an inconclusive 34-day war in 2006. That conflict killed a reported 1,200 to 1,300 Lebanese, including combatants, and 165 Israelis, including soldiers.