The officials said security forces have sealed off the village of al-Nawahid, in Qena province some 290 miles (465 kilometers) south of Cairo, to prevent the violence from spreading to neighboring towns. They said several people were arrested.
The attacks started after locals spotted a young Copt and a Muslim girl together at night inside the village cemetery, the officials said. They added that both were put under police custody as authorities investigate.
The officials spoke on condition of anonymity because they are not authorized to speak to the media.
Clashes between Christians and Muslims occasionally occur in southern Egypt, mostly over land or disputes over church construction. But sectarian tensions have also been on the rise recently in the capital.
Last year in Qena, a Coptic man was accused of kidnapping and raping a 12-year-old Muslim girl. The alleged assault led to widespread protests by the Muslim community and increased tensions between the two religious groups, which culminated in the murder of six Copts and one Muslim security guard at a church on January 6.
Coptic Christians make up about 10 percent of Egypt's population of 80 million. Copts and Muslims generally live in peace, though tension and violence occasionally flares.
Human rights groups say attacks on Copts are on the rise, underscoring the government's failure to address chronic sectarian strains in a society where religious radicalism is gaining ground.
The government insists Christians enjoy the same rights as Muslims.