The incident occurred on Wednesday in the staff colony of the Sui Southern Gas Company, a middle-class neighbourhood in Gulshan-e-Iqbal area in the city.
Police said the boy was accused by local residents of sending the allegedly blasphemous text message on Tuesday to employees and officers of Sui Southern Gas Company (SSGC) at the residential-cum-office compound, the Dawn newspaper reported.
After the news circulated among residents of the colony, a mob attacked the quarter of 16-year-old Ryan Stanten.
His mother, Rubina Bryan, works as a superintendent in Sui Southern Gas Company.
The boy and his mother were unharmed as they had left the quarter the previous night due to tension in the area.
"Had they not left the house, the situation could have been really bad," a senior police officer told the daily.
The mob ransacked the house and set fire to household articles, including a washing machine and a fridge, after bringing them out on the road. The protesters shouted slogans against the Christian family.
According to DIG Shahid Hayat, some local residents had gone to the boy and asked him about the SMS after receiving it. He told them that he had only forwarded the SMS after he had received earlier.
"Ryan told complainant Khursheed Alam and Pesh Imam Qari Ghulam Qadir of the SSGC Jamia Mosque that someone sent him this SMS and he forwarded it to all Muslim friends without reading it," said Mr Hayat.
"We reached the scene and talked sense to some clerics who were leading the protest," a police officer said.
Subsequently, an FIR was registered against the boy under Section 295-C of the Pakistan Penal Code, Section 7 of the Anti-Terrorism Act and Section 25 of the Telegraph Act.
Section 295 of the PPC is part of the harsh blasphemy law.
Human Rights Commission of Pakistan chief Zohra Yousaf described the incident as "very dangerous" as Christians were being targeted.
"At least 22 blasphemy cases have been reported in the country this year alone, in which Muslim accused are more in number compared to the Christians," she said.
In August, teenage Christian girl Rimsha Masih was falsely accused of blasphemy by a cleric in a neighbourhood on the outskirts of Islamabad.
She was released by the court and moved to an undisclosed location for security reasons after witnesses told a magistrate that the cleric had planted evidence to implicate her.
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