In a statement British Airways 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,"
They added: "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."
On flight monitoring service Flightradar, the plane was seen descending into Israel on schedule, before turning around and heading back in the direction of Greece.
According to the Israel Airports Authority, the choice to divert the plane was made by the pilot on board and the airport rejected suggestions it was unsafe to land at the airport.
Earlier today, Hamas sources announced they would be targeting Ben Gurion airport with rockets from the Gaza Strip.
British Airways is one of the few airlines operating flights to Israel outside Israeli carriers with the arrivals board of Ben Gurion airport showing several delays and cancellations.