CFG, which owns several top clubs including Manchester City, had acquired a 65% stake in Mumbai in 2019, with the club going on to win two league titles.
However, the ISL is in a state of limbo with the national governing body, the All India Football Federation (AIFF), struggling to find a new commercial partner after its 10-year deal with the previous one expired.
"The founding owners will assume full control of the organisation moving forward," Mumbai said in a statement on their official website.
"CFG has made this decision following a comprehensive commercial review and in light of the ongoing uncertainty surrounding the future of the Indian Super League."
The ISL was put on hold in July with stalled negotiations for a renewal of the AIFF's contract with its commercial partners, Reliance-led Football Sports Development Limited, cited as the reason.
Talks to renew the 2010 agreement came to a halt after India's Supreme Court asked the AIFF not to renew the deal with FSDL until it had issued an order over a separate case to implement a new constitution for the federation.