Mushtaq was arrested last May in a case filed under the Digital Security Act and charged with spreading disinformation against the government on social media.
The writer suffered a heart attack inside his cell at Kashimpur High Security Prison on Thursday evening, it was learnt.
He was transported to Shaheed Tajuddin Medical College Hospital, but declared dead on arrival, Senior Jail Superintendent Md Gias Uddin said.
"No apparent injury marks or other symptoms were found on his body during the autopsy. However, the cause of his death can be confirmed after conducting detailed examinations," Dr Safi Mohaimen, head of the Forensic Department of Tajuddin Medical College, said.
The body was handed over to relatives at 12:30pm.
Also read: Writer Mushtaq's death in custody triggers protests
Syed Bayezid, sub-inspector of Sadar police station under Gazipur Metropolitan Police, said, "Sores were found on his right hand and back. The wounds may have occurred when his body was transported to the hospital in the ambulance. However, it can be confirmed after receiving the autopsy report."
An unnatural death case has been filed with Gazipur Metropolitan Police's Sadar Police Station over Mushtaq's death in custody, Bayezid added.
Mushtaq's brother Dr Nafisur Rahman, who was waiting at the hospital morgue, stated: "I saw the body myself and did not notice anything unusual. An autopsy has been completed. What else can I say without having the autopsy report?"
The deceased writer's namaj-e-janaza would likely be held in Lalmatia after Maghrib prayers, and he would be laid to rest at Azimpur graveyard, according to Dr Nafisur.
Also read: Writer Mushtaq, arrested under DSA, dies in custody
The 53-year-old writer, who published the book Kumir Chaasher Diary under the pen name Michael Kumir Thakur, was picked up by RAB from his Lalmatia home on May 2, allegedly for posts critical of the government's handling of the coronavirus pandemic.
On August 20, he was shifted to the Kashimpur prison, Gias Uddin said.
Calls for Mushtaq's release were widespread and sustained throughout his time in prison. Soon after his arrest, more than 300 dignitaries in Bangladesh issued a joint statement demanding his release, alongside cartoonist Ahmed Kishore.
Amnesty International reiterated the demand in a statement as recently as January, saying the duo (Kishore and Mushtaq) had been arrested "solely for the peaceful exercise of their right to freedom of expression."
His applications for bail were turned down on at least four occasions.