According to jail officials, Singh, who was arrested over charges of illegal immigration in 2008, was suffering from cancer.
They said Singh, 28, was being treated at the Services Hospital for the past several days, but, his condition deteriorated on Tuesday, Oct 27.
Singh's body has been sent for an autopsy, The News reports.
The Pakistan Foreign Office has informed the Indian embassy about the incident and arrangements are being made for future action.
It is still not clear whether Singh's body will be brought back to India or not.