It also instructed the public administration ministry and the education secretary to submit the probe report within 30 days.
Justice FRM Nazmul Ahasan and Justice KM Kamrul Kader passed the orders on Monday after hearing a writ petition filed by Supreme Court lawyer Advocate Eunus Ali Akond.
Deputy Attorney General ABM Abdullah Al Mahmud Bashar argued for the state.
Enamul Karim, also the president of the governing body of Sonagazi Islamia Fazil Madrasa, reportedly failed to take action against the madrasa principal, SM Siraj-ud-Daula, following sexual abuse charges by Nusrat.
In a rule, the court also ordered the government to explain why inaction by Enamul Karim should not be deemed illegal.
The public administration ministry, education and home secretaries, the inspector general of police, the Feni deputy commissioner, the superintendent of police and the officer-in-charge of Sonagazi Police Station are the respondents to the rule.
Nusrat had been tricked onto the roof of the madrasa where the perpetrators set her on fire on Apr 6 for not withdrawing the sexual assault case against Siraj-Ud-Doula.
Nusrat’s brother Mahmudul Hasan Noman filed a case on the incident on Apr 8 naming eight people, including the principal as the main accused.
Nusrat died on Apr 10, five days after the attack, in a Dhaka hospital. Her death turned the attempted murder into a murder case.
On Jun 17, Bangladesh Cyber Crime Tribunal sent ex-Sonagazi police chief Moazzem to jail in connection with the murder of Nusrat following a police headquarters probe panel report.