Babu was sent to the private hospital in May this year following an order of the Bombay High Court.
Babu's lawyer Yug Chaudhry had told the court in May that he suffered from multiple ailments including a severe eye infection.
People are getting arrested as in the days of Indira Gandhi’s Emergency.
Babu tested positive for COVID-19 earlier this month and was initially brought from the Taloja prison in neighbouring Navi Mumbai to the government-run J J Hospital here.
Hany Babu moved the HC on Wednesday morning seeking medical aid for an eye infection that he developed after contracting COVID-19.
As per his family and lawyer, Delhi University's associate professor Hany Babu developed an acute eye infection on May 3, and is yet to receive appropriate medical care.
His wife has appealed to the authorities to shift him to a multi-speciality hospital where treatment for both his ailments can be given.
Babu was taken to government-run JJ Hospital here on Wednesday night from prison, the family said in a statement.
Chief Minister Pinarayi Vijayan on Wednesday said the state government has received a letter from Jenny Rowena seeking help.