Some affected passengers used social media to share pictures which appeared to show a letter handed out by British Airways with a similar message about security.
One frustrated customer posted a picture of a queue and said: "Currently about to board a British Airways flight to Cairo and it's cancelled.
"Not for two days, but for seven. Security risk. Someone knows something we don't."
One customer, Rasha, who asked to keep her surname private, said she was booked on a flight on July 25 but was alerted by text about the suspensions.
The IT worker, who is from Egypt and has lived with her family in Britain for six years, said she was supposed to meet her husband, children and other relatives.
"It's just terrible," she said. "It may seem like I'm just missing my flight for a holiday but I really need to go.
"I just want to know why do they have the right to cancel and not give at least an alternative?
"Now I'm running around not knowing what to do. I need to know why.
"Fair enough here is a political situation that is out of their hands, security, whatever, but at least offer a reroute. That's all. They have to offer a solution."
A spokeswoman for the airline said it could not immediately offer more information about the suspensions.
The airline was also among several major carriers to announce in June they would reroute flights to avoid the Strait of Hormuz.
The move - also taken by Australia's Qantas, Dutch carrier KLM, Emirates, Germany's Lufthansa, Malaysia Airlines and Singapore Airlines - followed the downing of a US drone by Iran.
