Nikhat (28) and her brother Nadeem (25), who were there to attend to their ailing mother, were burnt alive in the incident that took place at the Vinayak Orthopedics Centre in Civil Lines area of the district.
Around 30 people were present in the hospital when the incident occurred but all rest of them were safe, they said, adding that the patients were later shifted to an other hospital.
Fire tenders were rushed to the site and the blaze was doused within an hour, they said.
"A high-level inquiry has been ordered against the hospital administration and all its official documents have been seized," ASP (City) Mahendra Yadav said.