Hasan Nasr Allah was commenting on Israeli Security Minister Tzahi Hanegbi's weekend statement that there was a growing threat of such an attack.
Hanegbi said he did not know of a specific plot to attack the al-Aqsa mosque compound but intelligence assessments said the danger of such an action was growing.
The minister said "Jewish fanatics" might attack the mosque to act as "a catalyst for change to the whole political process".
Speaking on Hizb Allah's Al-Manar TV channel, he said: "The Israelis must be made to understand that the destruction of the al-Aqsa mosque would result in the destruction of the Zionist entity [Israel]."
The cleric said the warning had to be taken seriously because it came from "a member of [Israeli Prime Minister Ariel] Sharon's right-wing government, which certainly knows what is going on behind the scenes in Zionist extremism".
"We should not wait lazily until the event takes place, and then cry and beat our faces," Nasr Allah said.
"From today, positions should be taken, and messages sent, that will make them not even dare to think of embarking on such an act."
Hizb Allah resistance fighters fought against Israel's 18-year occupation of southern Lebanon, which ended with an Israeli military withdrawal in 2000.