Security and police officials said earlier that three Egyptians working together had killed one person and wounded three others in attacks on three churches and another man had been apprehended before attacking worshippers in a fourth church.
"[He] was apprehended as he tried to enter [a third church]," the ministry said in the statement. "The aforementioned is called Mahmoud Abdul Razik Salah Eddin Hussein," it said.
The ministry said Hussein had wounded three people in St George's Church and then wounded three others in Saints Church before being stopped trying to enter another church named after St George.
"The attacks ... led to six being wounded, one of whom died from his wounds," the ministry said, adding that Hussein suffered from mental illness and the attacks were under investigation.
A ministry official said Hussein's mental illness was the cause of the attacks and there was no political motivation.
The semi-official Middle East News Agency identified the victim as Nushi Atta Girgis, 78.
Egyptian riot police cordon off
one of the churches on Friday
The governor of Alexandria told Egyptian state television by telephone that Hussein, a supermarket employee, carried out the attack holding two knives and walked from church to church.
Abdul Salam Mahgoub, the governor, added that three of the people wounded in the attacks were in hospital but would leave later in the day.
About 600 Copts, mostly young men, gathered after the attacks to protest in the Sidi Bishr neighbourhood, outside Saints Church.
The area was ringed by about 200 riot police, and truckloads more were nearby.
Father Augustinos, who leads a different Mar Girgis Church, said the attacks occurred just after Mass began at 9am (0700 GMT).
"We are trying to calm the situation after many of our youth started protesting," Father Augustinos said. "We are telling them to calm down. It doesn't do any good for the country to make protests.
Alexandria is Egypt's second-
"We want to live in peace and tranquillity but these are people who had their family members killed or wounded," he said.
Copts account for up to 10% of Egypt's population of 73 million. They typically attend weekly Mass on Friday.
The United States condemned the attacks on the Coptic churches and urged both the Coptic and Muslim communities in Alexandria to exercise tolerance and calm.
"This act of violence against worshipers on a holy day for the Christian Coptic Community in Alexandria is unacceptable," said State Department spokesman Sean McCormack.
"We also would ask the Egyptian government to continue its efforts to defuse the situation, including providing effective security for all places of worship and calling upon people of all communities to refrain from further violence and incitement."
Egypt's last sectarian clashes were in Alexandria in October, when Muslims attacked churches and shops over the distribution of a DVD of a play deemed offensive to their religion. Four people were killed in week-long riots.