Those arrested have been identified as Manisha Pokharkar, Wasima Shaikh, Shital Shegokar, Surekha Gulve, Aarti Shingne and Bindu Naikde, a senior crime branch official told PTI.
Police had registered a case of murder against the jail officials and staff in connection with the death of the inmate, he said.
Shette (45) died at the government-run J J Hospital on June 23 after being allegedly beaten up by the jail officials and staff as she had failed to account for two eggs and five loaves of bread, which were distributed by her to the inmates, the official said.
All the six accused were already suspended by the jail department.
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After Shette's death, around 200 prisoners began a protest on June 24 for their demands, including allowing the media inside the jail premises.
During the protest some of the inmates went to the prison's roof, while others made a bonfire with newspapers and other documents inside the premises to express their anger.
Indrani Mukerjea, the prime accused in the Sheena Bora murder case, was among the 200 inmates of the Byculla jail who were booked by police for rioting and other offences after they staged a protest over Shette's death.
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