The court also asked the Jashore District and Sessions Judge to conduct the inquiry by an official not below the rank of district and session judge and submit the report within 60 days.
The virtual bench of Justice JBM Hasan passed the order after hearing a writ petition.
Barrister Humayun Kabir Pallab stood for the petitioner while deputy attorney general Samrendra Nath Biswas represented the state.
Barrister Humayun said earlier, a report from police said Imran was addicted to drugs.
On June 28, the HC asked the Jashore District Civil Surgeon to conduct a dope test of Imran. Later, the report from the civil surgeon said Imran was not addicted, he said.
As the two reports were contradictory, the HC ordered judicial inquiry into the matter.
Two lawyers, including Barrister Humayun filed a petition with the High Court seeking directive over judicial inquiry, compensation and bear the expenses of the medical treatment of Imran, whose kidney was damaged during torture by police.
According to the writ petition, Imran Hossain, son of Nesar Ali of Shahbazpur village in Sadar upazila of Jashore district has brutally been tortured by a policeman at Sajiali Police camp.
On June 9, a report on the incident was published at a daily newspaper.
Currently, Imran is undergoing treatment at a private hospital in Jashore and undergoing kidney dialysis since June 7 which is a sheer violence of the human rights of Imran.
On June 23, the High Court sought two reports from Jashore Civil Surgeon and superintendent of police which was submitted on June 28.
According to the report from Civil Surgeon, it is said that the kidney function of Imran is normal and he is physically fit while the report of police said Imran is a drug addict and they did not get any bruise on the body of Imran.
Besides, another report said three policemen took money illegally from Imran and released him.