The violence that took place on Thursday in the Nile Delta was the latest in a spate of vigilante killings in the region amid growing lawlessness since the 2011 revolution that toppled former president Hosni Mubarak.
Yussef Rabie Abdessalam, 16, pulled out a gun and opened fire indiscriminately, killing a passerby and wounding another after a heated argument with a man who had openly criticised the influential Brotherhood on the Internet, the sources said.
An angry mob surrounded the Abdessalam house seeking revenge, but the family refused to give Yussef up and hurled stones from inside the residence at the protesters.
A man outside the house was fatally wounded.
Police tried in vain to contain the violence and attempted to evacuate the Abdessalam family but the mob set fire to the house and in the confusion grabbed Yussef and lynched him.
"This is not a political incident," the Islamist party said, calling on all sides to show restraint.
But a security source and local media said the violence was triggered after comments hostile to the Muslim Brotherhood were posted on Facebook.
There have been several reports of lynchings in Egypt in recent months.
In March, villagers in Sharqiya province beat up a man and then lynched him, accusing him of car theft days after residents of another town strung up two men accused of kidnapping a girl.
