It also informed the Legislative Council that a probe had been ordered into the role of Deputy Inspector General (Prisons) Swati Sathe.
Shette died in Byculla Jail here on June 24 after she was allegedly beaten up inhumanly by the staff.
There was a heated debate on the incident in the Legislative Council today, with the opposition Congress, NCP and even the ruling ally Shiv Sena alleging that attempts were being made to shield someone in the government.
While replying to the debate, Minister of State for Home (Urban) Ranjit Patil announced suspension of Gharboodve, and jail superintendent Indulkar.
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He further announced that an Inspector General-level officer will probe the allegation that DIG Swati Sathe sent Whatsapp messages seeking financial and legal support for the six jail staffers arrested in the case.
"The probe against Sathe will deal with whether she should be made a co-accused," the minister said.
This probe will be conducted within a week, he added.
Leader of Opposition Dhananjay Munde (NCP) said that before the visit of opposition leaders to Byculla Jail after the incident, the authorities admitted Mariam Sheikh, an inmate and the complainant in the case, to hospital, so that she could not give them a first-hand account of events.
DIG Sathe should be made a co-accused, he demanded.
The women inmates who spoke to the opposition's delegation termed the conditions inside as "worse than hell", he said.