An unnamed security source was cited as telling Al-Masry Al-Youm that police had identified the victim as Fathy Ghattas, 71, from Cairo's middle-class Zeitoun neighborhood.
The paper cited the same source as saying investigators were probing reports that the gunman may have been a policeman.
Police arrested the man as he attempted to flee the scene, according to security officials.
Officials cited by the paper said the gunman had boarded the Cairo-bound train at the town of Samalout in Egypt's Minya province, roughly 260 kilometres south of Cairo.
The gunman allegedly checked passengers for the green cross traditionally tattooed on the wrists of Coptic Christians in Egypt. After identifying several Copts, he killed one of them and injured five others, several of them Christians, Al-Masry Al-Youm reported.
Other local media reports differed on the dynamics of the shootings, with some suggesting they were random and others that they followed a disagreement between Muslim and Christian passengers on the train.
Al-Masry Al-Youm said Egypt's state news agency Mena had confirmed the incident and reported that police were currently questioning the alleged gunman.
The motive for the gun attack was not immediately known, although the incident came less than two weeks after a suicide bomber killed 23 Christians and wounded nearly 80 others outside a church in the Mediterranean port city of Alexandria, some 250 km north of the capital Cairo.
Egypt announced earlier on Tuesday that it was recalling its ambassador to the Vatican over Pope Benedict XVI's comments urging the country to protect its Christian minority in the wake of the bombing.