No! For the course of MSc Data Science, its required that the student must have completed there UG education in Mathematics/Statistics. Also there are some institutes which allows allied subjects such as Physics graduates as well to be a part of the Data Science program.

If you are interested in Data Science and if you have interest in Psychology as well, then you can go for the course of MSc in Cognitive Science. The course of MSc Cognitive Science is a interdisciplinary course of Neuroscience, Physics, Data Science & Psychology which tries to find out logical footprints of day to day human interraction and have a lot of application in Robotics, AI, Sensor Technology etc.

For more information regarding MSc Data Science consider the link provided below:

https://www.careers360.com/courses/msc-in-data-science

I hope this helps. Wish you a great eve!