The arrested jail guard has been identified as Bindu Naikde. This is the first arrest in the case, a senior police official said.
Bindu was produced before a Mumbai court which sent her to police custody till July 7, the official added.
Shette (45) died at the government-run JJ Hospital on June 23 after being allegedly beaten up by jail staff after she failed to account for two eggs and five bread loaves, meant for distribution to inmates, said the official.
During the protest, some of the enraged inmates went to the prison's roof, while others made a bonfire of newspapers and documents inside the premises to express their anger.
Indrani Mukerjea, the prime accused in the Sheena Bora murder case, was among the 200 inmates booked by Nagpada police for rioting and other offences.
With regard to Shette's death, a complaint was filed and a case of murder was registered against jail staff, including Manisha Pokharkar, Wasima Shaikh, Shital Shegokar, Surekha Gulve and Aarti Shingne and Naikde, he added.