Egyptian police arrested 15 people in the aftermath of the clashes in the Mediterranean port town's Sidi Bishr suburb on Saturday.
Police arrested "some fanatic extremist elements who provoked skirmishes and threw stones at each other", the interior ministry said.
It said that the detainees, who included Copts and Muslims, "went too far" when they set two cars on fire and damaged several shops.
Some 15 people were injured and security forces used tear gas to disperse the crowd.
Security forces were deployed around the district to maintain calm on Saturday night.
Several hundred Copts attended the funeral of 78-year-old Noshi Atta Girgis who was killed by a knife-wielding assailant on Friday. At least five others were wounded in Friday's attacks on three churches in Alexandria.
Egyptian Copts typically attend weekly Mass on Friday, which is also the Muslim holy day and marks the beginning of the weekend in the country.
Saturday's funeral procession turned into a demonstration calling for Coptic unity.
The clashes erupted as the procession left the Quidissin church where the funeral service had taken place and headed to the nearby cemetery, the agencies said without being able to confirm who started the clashes.
Muslims and Copts attacked each other with sticks in Alexandria's downtown area and stones were thrown from nearby buildings.
"We want justice. Christ is the winner," they chanted as they marched through the city.
"Why can't we live in peace?" read a banner held by mourners at the funeral.
A car was set alight during the skirmishes and gunfire could be heard.
The demonstrators condemned the church attacks and demanded protection of Copts against what they called "oppression", Aljazeera said.
Security forces were quick to intervene and separated those who were fighting from the rest of the procession.
Men calm the son (C) of Noshi
Atta Girgis, who was killed
The Egyptian Interior Ministry said a 25-year-old man named Mahmud Salaheddin Abdul Razak had been arrested, describing him as "mentally unstable".
But Christian demonstrators in Alexandria said the authorities were trying to make excuses for what some Copts saw as increasing attacks by Islamists on Copts.
Police sources on Saturday told AFP that there were two attackers carrying knives, and put the number of wounded at 12.
Alexandria Judge Samy Breik ordered Abdul Razak to be held in custody for four days, charged with murder, illegal entry into a place of worship and illegal possession of weapons.
Witnesses said Abdul Razak shouted: "There is no god but Allah and Muhammad is the messenger of God," a statement that is one of the main tenets of Islam, as he carried out his attacks.
Egypt's Muslim Brotherhood in Alexandria denounced the attacks.
"We consider this crime an attack against all the Egyptian people, Muslim and Copt," a statement said, calling on security forces to protect places of worship.
It also warned against using the incident to "threaten the unity of the Egyptian people".
Separately, Aljazeera said, the Muslim Scholars Union condemned Friday's deadly assault and called for the perpetrators to be brought to justice.
Grieving Coptic Christians at the
funeral procession in Alexandria
The US administration has condemned the attack and urged the Coptic and Muslim communities of Alexandria to exercise tolerance and restraint.
Copts make up about 10% of Egypt's mostly Muslim population of 73 million.
Coptic faithful, religious leaders and intellectuals expressed fear of further harassment after the gains of the Muslim Brotherhood in parliamentary elections last autumn.
Security forces' failure
Muslim Brotherhood spokesman Issam al-Aryan expressed disbelief over the security forces' failure to prevent the attack.
"It's very sad news. I cannot understand what the security and police were doing. They are supposed to be guarding the churches," al-Aryan said.
The deadliest recent communal clashes occurred in October, when Muslim protesters attacked a church in Alexandria that they said hosted a play they deemed offensive to Islam. Three people were killed in the fighting.
A 19-year-old Muslim who stabbed a nun during the rioting was sentenced to three years in jail in February.