The airport has been fully operational since Israel began an aerial offensive on Tuesday in the Gaza Strip and Palestinian militants intensified their cross-border rocket fire. International airlines have continued to fly in, despite now-daily rocket salvoes at Tel Aviv that either have been intercepted by Israel's Iron Dome missile defence system or hit areas where they caused no casualties.
"The armed wing of the Hamas movement has decided to respond to the Israeli aggression, and we warn you against carrying out flights to Ben-Gurion airport, which will be one of our targets today because it also hosts a military air base," said a statement by the Islamist group's Izz el-Deen al-Qassam Brigades.
The group, which said it had issued the warning to airlines so that injury to their passengers could be avoided, announced earlier that it had already fired at least one rocket towards the airport on Friday.
A spokesman for Israel's Airports Authority said a siren had sounded at Ben-Gurion and that all activity had stopped for about 10 minutes, but that it was part of a general alert in the Tel Aviv area and not a direct threat to the airport.
Projectiles launched by Gaza militants are largely inaccurate and there have been no reports of any landing in or close to the airport, located in an area covered by the Iron Dome system. But the rockets have been striking deeper into Israel, reaching areas more than 100 km (60 miles) north of the Gaza Strip.
At the start of the Israeli offensive on Tuesday, takeoffs and landings at Ben-Gurion were re-routed to more northerly flight paths.
At least 88 Palestinians have died during Israel's four day-old air and sea offensive on Gaza as it attempts to halt the rocket fire.