The Israeli military said "several attempts were made to intercept" the missile that was launched from Yemen, a rare Huthi attack that penetrated Israel's air defences.
An official told AFP the country's security cabinet would convene in the evening.
A police video showed officers standing on the edge of a deep hole in the ground with the control tower visible behind them. No damage was reported to airport infrastructure.
The police reported a "missile impact" at Israel's main international gateway.
An AFP photographer said the missile hit near the parking lots of Terminal 3, the airport's largest. The crater was just hundreds of metres (yards) from the tarmac.
"You can see the area just behind us: a crater was formed here, several dozen metres (yards) wide and several dozen metres deep," central Israel's police chief, Yair Hezroni, said in the video.
The Israel Airports Authority said: "This is the first time a missile has fallen so close to the terminal and the runways."
It was not immediately clear whether the impact was caused by the Yemeni missile or by an interceptor.
The attack was claimed by the Huthis, who say they act in support for Palestinians in war-ravaged Gaza.
"The missile force of the Yemeni armed forces carried out a military operation targeting Ben Gurion airport" with a "hypersonic ballistic missile", the rebels said, referring to their forces.
Defence Minister Israel Katz threatened a forceful response, saying: "Anyone who hits us, we will hit them seven times stronger."
- 'Take shelter' -
Palestinian militant groups Hamas and Islamic Jihad later hailed theattack on the airport.
Israel's Magen David Adom emergency service said it had treated at least six people with light to moderate injuries.
An AFP journalist inside the airport at the time of the attack said he heard a "loud bang" at around 9:35 am (0635 GMT), adding the "reverberation was very strong".
"Security staff immediately asked hundreds of passengers to take shelter, some in bunkers," the AFP journalist said.
"Many passengers are now waiting for their flights to take off, and others are trying to find alternative flights."
An incoming Air India flight was diverted to Abu Dhabi, an airport official told AFP.
It was one of the airlines to suspend Tel Aviv flights until May 6, along with Germany's Lufthansa Group, which includes Austrian, Eurowings and SWISS.
A passenger said the attack, which came shortly after air raid sirens sounded across parts of Israel, caused "panic".
"It is crazy to say but since October 7 we are used to this," the 50-year-old, who did not want to be named, said referring to the 2023 Hamas attack on Israel that sparked the Gaza war.
An airline official said: "Today was a close call".
"I have worked at the airport for several years but even I was afraid today," they told AFP.
Flights resumed after being halted briefly, with the aviation authority saying Ben Gurion was now "open and operational".
- Deadlock -
Israel's security cabinet would meet on Sunday, a government official said, after media also reported a planned expansion of the Gaza war with call-up orders issued for tens of thousands of reserve troops.
Several news outlets said the military had begun sending the orders for reservists to replace conscripts and active-duty soldiers in Israel and the occupied West Bank so they can be redeployed to Gaza.
A military spokesperson neither confirmed nor denied the reports but Israel's public broadcaster said the security cabinet would meet to discuss the expanded offensive.
The Huthis, who control swathes of Yemen, have launched missiles and drones targeting Israel and Red Sea shipping throughout the Gaza war. They say they are acting in solidarity with Palestinians.
Israel resumed major operations across Gaza on March 18 amid deadlock over how to proceed with a two-month ceasefire that had largely stopped the war sparked by Hamas's October 2023 attack.
Sunday's attack on Israel was the fourth the Huthis have claimed in three days.
Israel has intercepted most of the Huthi missiles fired since the Gaza war started.
In March, the Huthis threatened to resume attacks on shipping over Israel's aid blockade on Gaza after a suspension of attacks during the truce.
The US military has been hammering the rebels with near-daily strikes since March 15.
ha-csp/dv
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