The rockets launched by Hamas over Israel had intercepted by the Iron Dome missile shield, with no casualties being reported.
Late on Tuesday, the military said that an undefined "projectile" was sacked from Gaza towards southern Israel.
The previous such announcement was on October 30, when Israel blew up a tunnel dug by Islamic Jihad. A third projectile hit an open area in southern Israel.
The rocket that fell short destroyed an empty classroom in Beit Hanoun's Ghazi al-Shawa public school, according to the IDF.
"In response to the rocket fired from the Gaza Strip at Israel earlier today, the IAF targeted a Hamas military compound in the southern Gaza Strip", said the IDF Spokesperson Unit.
The bombardment came after a rocket fired toward Israel's southern coastal city of Ashkelon was intercepted by the anti-missile Iron Dome defense system.
He did not elaborate on how Israel knew Hamas was responsible for the tunnel, which he said reached to within 1km (0.6 miles) of the nearest Israeli civilian community.
The army did not say when the crossings would reopen.
According to other sources, Iranian Revolutionary Guards commander Qassem Soleimani has urged Hamas to fire rockets at Israel.
In the last few days IDF had targeted Hamas positions in the Gaza Strip several times.
Protesting US President Donald Trump's declaration that Jerusalem is the Israeli capital, terror group Hamas, which runs Gaza and seeks Israel's destruction, called for a new intifada and vowed to liberate Jerusalem.
The Israel-Gaza tensions have apparently been fed by Washington's recognition last week of Jerusalem as Israel's capital.
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