MBA in shipping and port management is a great course for students who want to pursue a different kind of management post. But after a comprehensive search I don't get any college offering the course in Mumbai. I am mentioning some of the name of the college which are scattered in different parts of India and are said to be the best for the subject:

Indian Maritime University, Kochi Campus

MIT College of Management, Pune

Indian Maritime University, Chennai

International Maritime Academy, Chennai

For more colleges offering the course you may visit the link below:

https://bschool.careers360.com/colleges/list-of-mba-in-port-and-shipping-management-colleges-in-india

I hope this answer helps. All the very best for your future endeavors!