Israeli military spokesman Jonathan Conricus said the tunnel belonged to Palestinian Islamist movement Hamas, which runs the Gaza Strip, and was intended for attacks as opposed to smuggling.
Such tunnels have been used to carry out attacks in the past.
He said he was not aware of any casualties from the destruction of the tunnel, which was still being built.
It ran underneath the main goods crossing between Israel and the blockaded Gaza Strip -- known as Kerem Shalom -- as well as gas and fuel pipelines, he said. The crossing was to remain closed until further notice.
According to Conricus, Israeli air strikes late Saturday along with other unspecified means were used to destroy the tunnel.
The strikes occurred within the Gaza Strip, while further means were used in Israeli territory.
The tunnel began east of the city of Rafah in the Gaza Strip, crossed into Israel some 180 metres, then continued into Egypt for an unspecified length, with no exit point detected, he said.
Conricus said Israel had coordinated with Egypt on the operation.
The tunnel stretched a total length of around a kilometre and a half, he said.
Defence Minister Avigdor Lieberman said: "Destroying the network of offensive tunnels is an essential component in our policy of systematically damaging the strategic abilities of Hamas."
"The message to the Gaza leadership and residents is clear -- invest in life and not burial tunnels," Lieberman said in a statement.
Hamas had not commented on the Israeli operation.
It is also building an underground wall in the area around the Gaza Strip to stop such tunnels.
The latest tunnel was at least the third destroyed since late October by Israel -- some Israeli media reports say a fourth was also destroyed recently -- but it comes at a particularly sensitive time.
Tensions between Palestinians and Israel have been high since US President Donald Trump's recognition of Jerusalem as Israel's capital on December 6.
Unrest has included rockets being fired from the Gaza Strip into Israel, with Israel's military responding with air strikes.
Rocket fire is often claimed by fringe Islamic radical groups in the Gaza Strip, but Israel holds Hamas responsible for all such acts.
Conricus said Sunday Israel was defending its sovereignty with the destruction of the tunnel and was not seeking an escalation.
On October 30, an Israeli operation to blow up an Islamic Jihad tunnel stretching from the Gaza Strip into its territory left 12 Palestinian militants dead.
Israel is holding the bodies of five of the militants.
Hamas and Israel have fought three wars since 2008, and the last conflict in 2014 was waged in part over tunnels from Gaza that were used to launch attacks.
Egypt has also destroyed smuggling tunnels stretching from the Gaza Strip into its territory.
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