It comes after reports that Palestinian militant group Hamas had fired multiple rockets towards Ben Gurion Airport.
A British Airways spokesman said: “Safety is always our highest priority and following the latest assessment of the situation, we’re suspending our flights to and from Tel Aviv.
“We’re contacting customers booked to travel to or from Tel Aviv to apologise for the inconvenience and offer options including a full refund and rebooking with another airline or with British Airways at a later date.
“We continue to monitor the situation in the region closely.”
Other carriers suspended services to and from Tel Aviv after the Hamas attacks on Saturday, meaning UK citizens trying to fly home from Israel face a struggle to book flights.
EasyJet usually serves Gatwick, Luton and Manchester airports from the Israeli city but has paused operations on those routes.
Wizz Air, which normally connects Israel with Gatwick and Luton, has also suspended those flights.
Virgin Atlantic has taken the decision to pause flying to and from Tel Aviv for the next 72 hours.
It said: “As the dynamic situation evolves, we’ll keep our flying programme under constant review. Our teams will be in contact with any affected customers to discuss their options, which include rebooking to a later date or a full refund.
“We would advise anyone booked to travel to check their flight status on the website before travelling to the airport.”
The Government has not provided an estimate on how many UK citizens are in Israel.
A travel industry source said the number of UK tourists in Israel is low.
Israel’s ministry of tourism said it is “committed to ensuring that all tourists visiting Israel are safe and informed”.
It added it is operating a “hotline via WhatsApp for tourists” on +972 55 972 6931.