"The safety and security of our passengers and crew is our number one priority and all affected passengers will be contacted via email or text."
Meanwhile, Virgin Atlantic said it had paused flights between Tel Aviv and London Heathrow for the next 72 hours.
"As the dynamic situation evolves, we'll keep our flying programme under constant review," they said, adding staff would contact impacted customers to discuss options which include rebooking to a later date or a refund.
British Airways said in a statement that it was suspending flights to and from Tel Aviv "following the latest assessment of the situation".
"Safety is always our highest priority," they added, apologising to customers booked to travel to or from the Israeli city for the inconvenience and promising to rebook or refund them.
"We continue to monitor the situation in the region closely," the airline concluded.
Israeli flag carrier El Al said it was maintaining its Tel Aviv flights for now. “We might cancel flights to places where we don’t have a lot of Israelis to help other Israelis in other places,” a spokeswoman said.
Israel Airports Authority said on its website that Ben Gurion continued to handle arrivals and departures.
Regulators including the United States' Federal Aviation Administration, the European Union Aviation Safety Agency and Israel's aviation authority urged airlines to use caution in the region's airspace but stopped short of suspending flights.
Israel's civil aviation authority asked airlines to "review current security and threat information" amid the conflict and changed some air traffic routes. It noted that delays were expected and advised airlines to carry extra fuel.
Meanwhile, thousands of young Israeli men have been scrambling to return to Israel to serve in the IDF as reservists whilst others have already returned after arriving on flights to Ben Gurion on Monday.
El Al has been arranging rides to soldiers’ homes, military bases or units for those who need them from Ben Gurion.
It comes after the Israel Airports Authority said a Hamas rocket salvo aimed at the Tel Aviv area on Monday did not lead to any impacts at Ben Gurion.
Videos which had been circulating online appear to show smoke rising from Israel's main international gateway.
