Christians comprise up to 10 per cent of Egypt's roughly 75 million people, with the remainder being primarily Sunni Muslim.
Relations between Muslims and minority Coptic Christians in Egypt are generally peaceful despite sporadic violence.
However, restrictions on building churches have been one of the main grievances of the Coptic Christian community.
A spokesman for Egypt's interior ministry confirmed that around 500 Muslims had gathered after Friday prayers, and that the entrances to three homes had been set on fire.
He said three people were hurt in the commotion but declined to characterise it as a clash.
One security source said Christians in Behma were expanding a house that was used informally for prayer, although others said the Christians were constructing a new church from scratch.
The sources could not immediately say whether the Christians had obtained proper building permits.
Security sources said rumours that the Christians did not have a permit for church construction, had sparked anger among Muslims.
This turned to violence after prayers when about 300 Muslims clashed with a group of about 200 Christians.
The two sides fought each other with sticks and threw bricks and firebombs, the sources said, and between 10 and 20 houses and shops were set on fire, including several shops that sold wood and construction materials.
Police intervened to stop the clashes, arresting 17 people from both faiths and sealing off the village, they said.
History of clashes
Egypt suffered its worst Christian-Muslim clashes in decades in 1999, when 20 Christians were killed, 22 people wounded and scores of shops destroyed in sectarian strife in the southern village of Kosheh.
In February, Muslims set fire to Christian-owned shops in southern Egypt after hearing rumours of a love affair between a Muslim woman and a Coptic Christian man.
Last year, a 45-year-old Muslim man stabbed a Coptic Christian man to death and wounded five others in the Mediterranean city of Alexandria, sparking three days of clashes in which one Muslim was killed.
Egypt says the attacker was mentally ill.