I am from Mumbai. I am working professional

Eligibility for getting admission in a full-time MA course (2 years) is having a bachelor's degree in any stream. However, there are some institutes that do not allow people from other streams for this course. You can apply to autonomous colleges in the city after checking their respective criteria (varies from college to college). You cannot apply to Mumbai University for a full-time course because it allows only people with a three year BA degree to apply for MA in psychology.

However, since you are a working professional, the best option for you would be doing the course through distance learning and correspondence. There are many open universities all over the country that provide distance learning courses like The University Of Mumbai, IGNOU etc. Universities providing MSc in Psychology via distance learning are Madras University, Tamil Nadu Open University etc. Check the official sites for more information on the same.