Though there are no post graduate courses like MD in Genetics following MBBS, you may pursue an MD in pathology which offers courses of Molecular genetics and molecular hematology.

Or you may also pursue a course in Master of Sciences (MSc.) in genetics. Genetics is currently an very lucrative field with the whole world focusing on increasing funds towards research.

You  may find more information regarding genetic courses and colleges available in the link below:

https://www.careers360.com/courses/genetics-course

In most Foreign Universities as well as most IITs and IISc Bangalore, MBBS is considered as any other Bachelors Degree like B.Tech or BS/B.Sc.

If seriously interested in genetics, you can always pursue research in Top Universities and pursue a Masters or Doctoral Degree with focus on Genetics.

Most of the Top Universities like UC Berkeley, Harvard, Stanford, CalTech, Oxford as well as NUS Singalpore and Nanyang Technological University, Singapore have excellent research groups focussed on Genetics, Bioinformatics and several other relevant research fields.

For more information do follow the link below

https://www.careers360.com/courses/genetics-course