The attackers set hurled stones and set fire to several shops, smashed windows of a church and damaged two cars in the early morning hours before the shops in Isna were opened for business, said the police official, who spoke on condition of anonymity because he was not authorized to talk to the media.
Police detained 15 people suspected of taking part in the attacks in Isna, located about 350 miles south of Cairo, he said.
The riots followed reports that two Coptic Christians pulled down the veil of a Muslim woman in a car park on Saturday evening. Dozens of Muslims started to gather in protest very early Sunday, but police managed to disperse them.
Police blocked all main streets leading to the town, but witnesses said some people managed to attack the shops in two of the town's streets. Peace returned to the town after several hours of rioting, they said.
Earlier this week, dozens of Muslims went on a rampage following rumors of an attempt of abduction and sexually assault a teenage Muslim girl by some Coptic Christians. The rioters hurled stones and smashed windows of a pharmacy were they suspected the Copts forced the girl to have sex with them.
On Thursday, police arrested two Coptic Christians suspected of taking part in the abduction of the girl. They were ordered detained for 15 days on charges related to sectarian tensions, police said.
Muslim-Coptic tensions are commonplace in southern Egypt, mostly over land or church construction disputes.
On New Year's Day in 2000, a dispute between the Muslims and Copts in the mixed village of Kosheh escalated into a clash with groups of armed villagers shooting at each other, leaving 21 Christians and one Muslim dead.
Coptic Christians make up an estimated 10% of Egypt's 76.5 million people and generally live in peace with the Muslim majority. The government is highly sensitive to public discussions of its treatment of the Coptic minority, insisting Christians enjoy the same rights as the Muslim majority.