Cairo International Airport administration called the British airline's decision an "internal matter", according to the Egyptian daily Al-Shorouk.
Some passengers were only informed of the news after already arriving at London Heathrow airport for their flight.
On Friday, the British Foreign Office warned people of "heightened risk of terrorism against aviation", and said additional security measures had been taken for the flights from Egypt.
"As safety is the number one priority of Lufthansa, the airline has temporarily suspended its flights to Cairo today as a precaution, while further assessment is being made", Lufthansa said in a statement.
Current Foreign and Commonwealth Office advice on travel to Egypt warns against "all travel" to certain parts of the country.More news: Did DOJ Save Trump In Stormy Daniels Case?
"Now I'm running around not knowing what to do".
"It's just awful", she said.
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. "Additional security measures are in place for flights departing from Egypt to the United Kingdom", the British advisory says.
"I just want to know why do they have the right to cancel and not give at least an alternative?"
The Egypt State Information Service could not immediately be reached for comment.
It adds: "Additional security measures are in place for flights departing from Egypt to the United Kingdom".More news: Trump relished rally chant, Ocasio-Cortez tells constituents in Queens
The Foreign Office has not issued warnings against air travel to and from Cairo, but has advised against all non-essential travel to the Egyptian resort of Sharm el-Sheikh.
"This is unusual in aviation and it does suggest BA have received either intelligence or notification in their ongoing security assessments of airports they fly to, something that perhaps they haven't liked and has triggered this immediate suspension".
The agency said an estimated 415,000 British nationals visited Egypt in 2018 and that most visits were "trouble free".
The airline was also among several major carriers to announce in June they would reroute flights to avoid the Strait of Hormuz.
BA is one of only two airlines that fly nonstop between United Kingdom and Cairo.More news: Crypto Exchange BitMEX Under Investigation by CFTC