At least another five people were reported to have been injured in the shooting on a train between Assiut and Cairo.
One official was quoted as saying those injured included Muslims.
The gunman, who officials said had boarded the train at Samalut, has been arrested.
The Egyptian interior ministry named the gunman as police officer Amer Ashour Abdel-Zaher. Officials have not given a motive for Tuesday's shooting.
The ministry statement said the officer "opened fire on some train passengers from his pistol and ran away", adding that he was later arrested at his home.
One of those injured was reported to be the dead man's wife.
A bomb attack on a Coptic Christian church in Alexandria at the new year killed 23 people.
Egypt's Coptic Christian minority makes up between 7% and 14% of Egypt's 80 million people.
The BBC's Jon Leyne reports from Cairo that it is difficult to see how the gunmen would have known he could target Christians by boarding the train.
http://www.bbc.co.uk/news/world-middle-east-12165523
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