In a meeting with UK ambassador Geoffrey Adams, Younes al-Masri voiced his "displeasure" that the airline's "unilateral decision" had been taken "without consulting Egyptian authorities", according to a ministry statement.
The British carrier said Saturday it had halted flights for a week following a security review, without giving further details.
German carrier Lufthansa, which had also suspended flights to Cairo from Munich and Frankfurt on Saturday without giving a reason, resumed operations Sunday.
Adams apologised to Masri for the fact that Egyptian authorities had not been notified, the ministry said.
The ambassador said BA's decision had "nothing to do with the security measures of Egyptian airports", adding that both sides were working to "solve this problem as soon as possible", the statement added.
The ministry said on Saturday it was "coordinating" with the British embassy in Cairo and BA's local representative, as well as running extra EgyptAir flights to London to carry stranded passengers.
In its travel advice for British nationals heading to Egypt, the UK Foreign Office warns of "a heightened risk of terrorism against aviation".
Tourism is a vital source of revenue and jobs for the North African country, but has been battered by deadly attacks targeting foreigners and security forces since the 2011 uprising that toppled longtime ruler Hosni Mubarak.
Britain cancelled flights to Egypt's Sharm El-Sheikh in 2015 after jihadists bombed a Russian airliner carrying holidaymakers from the Red Sea resort, killing more than 220 people on board.
But the sector has partly recovered since, with an estimated 415,000 British nationals visiting Egypt in 2018.