Yes, there is a masters degree in design ie M. Des
The eligibility critera in order to pursue Master of Design, one need to have a Bachelor of Design or Bachelor of Architecture degree with a minimum of 50% marks in some colleges. Whereas in some colleges the eligibility criteria is less strict and youd be required to have any bachelors degree minimum 3 years duration to be eligible. Hence the criteria would depend on college to college. Various colleges to pursue are NID, NIFT, IITs etc
Best of luck.