Thirteen members of the family in Lahore have been threatened with being burnt alive over the incident.
It's reported local Muslim became furious when news of the affair emerged. They threatened to abduct and kidnap Christian girls from the area and burn them alive if the Muslim woman is not returned to the family.
CLAAS UK, a charity helping persecuted Christians in Pakistan, said Christian residents are living in fear but the police have taken no action.
Nasir Saeed, Director CLAAS-UK, said such incidents rarely occur but if they do then the extended family, and sometimes the local Christian community, has to pay the price for one individual's actions.
Mr Saeed said: "Unfortunately, in Pakistani society, Christians are looked upon with hatred and as inferior to the Muslims. Therefore, such incidents are never tolerated. Growing hatred and intolerance against Christians makes it even worse.
"Everyday several Christian girls - some under age - are kidnapped, abducted, and/or forcibly converted to Islam but the government and even courts fail to do justice with Christian and Hindu families."