Sinh was admitted to the Woodburn Ward of SSKM hospital after he complained of illness, the police said.
He failed to appear before the Alipore court on Friday due to illness. He was discharged from the SSKM hospital on Thursday and sent to jail custody.
Sinh was remanded in jail custody on "paper production" by the CBI, a day after his arrest.
The Special Crime branch of CBI had arrested Sinh in connection with the ongoing investigation into the multi-crore Saradha chitfund scam on January 31 and was charged with criminal conspiracy and cheating in the Saradha Realty case.
The former Congress MP from Assam had been earlier questioned by the Enforcement Directorate (ED) in connection with the Saradha case in New Delhi.