A gunman fired at worshippers and Egyptian police stationed outside a Coptic Orthodox church near Cairo and killed nine people before being wounded and arrested.
The so-called Islamic State group said it was behind the attack.
The Coptic Church said the gunman first shot at a Christian-owned shop 4km away, killing two people, before proceeding to the Mar Mina church in the southern Cairo suburb of Helwan.
The Interior Ministry said he opened fire at the entrance to the site and tried to throw an explosive device.
Eleven people were killed in all, including a policeman at the church, according to Interior Ministry and Coptic Church accounts.
The ministry added that investigators had identified the gunman and that he had carried out several attacks since last year.
Security forces are on high alert for Christmas and New Year celebrations. Egypt is also grappling with a deadly IS insurgency in the North Sinai region.
Islamist militants have said they were behind several attacks on Egypt's large Christian minority in recent years, including two bombings on Palm Sunday in April and a blast at Cairo's largest Coptic cathedral in December 2016 that killed 28 people.
