Omar Khalid, a grade VI student of the Government MC School at Yasinabad in Faisalabad district, 100 kilometres from Lahore, was reportedly upset following his expulsion from school.
Doctors described the boy's condition as critical. They said he had suffered 90 per cent burns and his chances of survival were remote.
Omar is the only child of Khalid Ahmed, a butcher.
The boy was rushed to a hospital with severe burn injuries and the father too was admitted a little later after he suffered a heart attack.
Ahmed told reporters that his son was expelled from school for being absent for a few days.
"Today he asked me to accompany him to the school as the headmaster told him not to come to school without his father," Ahmed said.
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He added that he had refused to go to the school with his son because he had faced embarrassment in the past when the headmaster complained about Khalid's lack of interest in studies.
"After this, my son left the house and set himself on fire after pouring oil on himself," Ahmed said.
Several of Khalid's classmates visited the hospital to inquire about his health.