Some 71 people were wounded in the blast, which struck at a Coptic Church in the Nile Delta City of Tanta, 120 kilometres (75 miles) north of Cairo, according to a health ministry toll.
Images broadcast by private television stations showed bloodstains smearing the whitewashed walls of the church next to shredded wooden benches.
Palm Sunday is one of the holiest days of the Christian calendar, marking the triumphant entrance of Jesus to Jerusalem.
“The explosion took place in the front rows, near the altar, during the mass,” General Tarek Atiya, the deputy to Egypt’s interior minister in charge of relations with the media, told AFP.
There was no immediate claim of responsibility for Sunday’s blast.
Copts, who make up about one tenth of Egypt’s population of more than 92 million and who celebrate Easter next weekend, have been targeted by several attacks in recent months.
Pope Francis is due to visit Cairo on April 28-29 to show solidarity with Egypt’s Christian community.
Jihadists and Islamists accuse Copts of supporting the military overthrow of Islamist president Mohamed Morsi in 2013, which ushered in a deadly crackdown on his supporters.
In December, a suicide bombing claimed by the Islamic State group killed 29 worshippers during Sunday mass in Cairo.
The bombing of the church within a compound that also holds the seat of the Coptic papacy was the deadliest attack against the minority in recent memory.
A spate of jihadist-linked attacks in Egypt’s restive Sinai Peninsula, including the murder of a Copt in the city of El Arish whose house was also burned, have led some Coptic families to flee their homes.
About 250 Christians took refuge in the Suez Canal city of Ismailiya after IS released a video in February calling for attacks on the religious minority.
Foreign Ministry spokesman Ahmed Abu Zeid called Sunday’s bombing “a failed attempt against our unity”.
“Terrorism hits Egypt again, this time on Palm Sunday,” he tweeted.
String of attacks
Prime Minister Sherif Ismail also condemned Sunday’s apparent attack, stressing Egypt’s determination to “eliminate terrorism”.
The Cairo-based Al-Azhar, an influential Sunni Muslim authority, said Sunday’s bombing aimed to “destabilise security and… the unity of Egyptians”.
Egypt’s Copts have endured successive attacks since Morsi’s ouster in July 2013.
More than 40 churches were attacked nationwide in the two weeks after the deadly dispersal by security forces of two pro-Morsi protest camps in Cairo on August 14, 2013, Human Rights Watch said.
Amnesty International later said more than 200 Christian-owned properties were attacked and 43 churches seriously damaged, adding that at least four people were killed.
President Abdel Fattah al-Sisi, who as then army chief helped remove Morsi, has defended his security forces and accused jihadists of attacking Copts in order to divide the country.
In October 2011, almost 30 people — mostly Coptic Christians — were killed after the army charged at a protest outside the state television building in Cairo to denounce the torching of a church in southern Egypt.
In May that year, clashes between Muslims and Copts left 15 dead in the working-class Cairo neighbourhood of Imbaba where two churches were attacked.
A few months earlier, the unclaimed bombing of a Coptic church killed more than 20 people in Egypt’s second city of Alexandria on New Year’s Day.
Pope Francis will visit the site of the December church attack next to Saint Mark’s Coptic Orthodox Cathedral — the seat of Coptic Christian Pope Tawadros II.