As per a prison official, they didn't receive the release order by 5:30 pm, the deadline set by jail authorities, hence the couple was not freed on Monday.
Earlier, their lawyer said the Kochhars were unlikely to walk out of the prison during the day.
The couple was arrested by the Central Bureau of Investigation (CBI) on December 23 for their alleged roles in the fraud case and are currently in judicial custody.
Deepak Kochhar is lodged in Arthur Road Jail in central Mumbai, while Chanda Kochhar is housed in the nearby Byculla women's prison.
Earlier in the day, the High Court granted interim bail to the couple and came down heavily on the CBI for making the arrest in a "casual and mechanical" manner and without application of mind.
The CBI named the Kochhars, Videocon group founder Venugopal Dhoot along with Nupower Renewables (NRL) - managed by Deepak Kochhar - Supreme Energy, Videocon International Electronics Ltd and Videocon Industries Ltd as accused in the FIR (first information report) linked to the case registered in 2019 under Indian Penal Code sections related to criminal conspiracy and provisions of the Prevention of Corruption Act (PCA).
The central agency has alleged that ICICI Bank, headed by Chanda Kochhar from 2009 to 2018, sanctioned credit facilities to the tune of Rs 3,250 crore to these companies in violation of norms.
It further claimed that as a part of quid pro quo (Latin expression literally meaning "something for something"), Dhoot made an investment of Rs 64 crore in Nupower Renewables through Supreme Energy Pvt Ltd (SEPL), and transferred SEPL to Pinnacle Energy Trust managed by Deepak Kochhar through a circuitous route between 2010 and 2012.