Speaking to , SFI President Digambar Kamat said that he had sought a report from the state body about the incident.
"We have taken a suo moto step after the video surfaced online. We don't yet know where the incident took place, but we are trying to find out," Kamat said.
Late on Wednesday, filmmaker Vinod Kapri uploaded grabs of the video and tagged Sports Minister Kiren Rijuju, seeking action against the coach.
Rijiju tweeted in response: "A stringent action will be taken through Sports Authority. Firstly, it's a heinous crime of serious nature so I'll urge the Police to take stringent penal action against the coach urgently."
On Thursday, Rijiju directed the SFI to ensure that the "coach is not employed anywhere in India".
"I've taken a strong view of the incident. The Goa Swimming Association has terminated the contract of coach Surajit Ganguly. I'm asking the Swimming Federation of India to ensure that this coach is not employed anywhere in India. This applies to all Federations and disciplines," Rijiju tweeted.
Goa's Director of Sports and Youth Affairs, V.M. Prabhudessai, also said that Kamat had verbally communicated to him about the termination of the chief coach's services.
"Kamat has just informed me about the decision to terminate the services of the chief coach," Prabhudessai said.
Surajit Ganguly could not be contacted for his response despite several attempts.
( With inputs from IANS )