Muhammad Abul-Kasem, 19, originally from Manchester, was detained in the country on 21 November.
A relative told the BBC he was arrested upon his arrival from Libya after authorities found a photograph of a military aircraft on his mobile phone.
The Foreign Office confirmed a British man had been arrested in the Egyptian port of Alexandria.
Mr Abul-Kasem’s family told BBC Asian Network the photograph had been taken through an aeroplane window as it came to land at Alexandria airport.
They said he now faces charges of spying, although no details have been confirmed by Egyptian authorities.
Mr Abul-Kasem had been living in Libya for the past two years, where his father is from, the family said. His mother is from Pakistan.
The Foreign Office said it was seeking more information.
“Our staff are providing assistance to his family,” a spokesman said.