Yes, most universities in India, including those outside Mumbai University, offering MSc Physics programs will have an entrance exam for students who are *not* from that university. The specific exam varies from university to university. Some may use a common entrance exam like the JAM (Joint Admission Test for MSc), while others have their own university-specific entrance tests. Some universities might also consider your undergraduate marks and performance.
To find out the exact entrance exam requirements, you need to check the official websites of the specific universities you're interested in applying to. Look for their MSc Physics program page, usually under "Admissions" or "Academics." The admission criteria will be clearly stated there.