You can do M.Sc. Biotechnology. It is a 2-year long course divided into 4 semesters. The minimum eligibility criterion needed to be fulfilled for pursuing the course is graduation in any of Biology, Math, and Chemistry. 
M.Sc. Biotechnology: Eligibility 
As a minimum criterion of eligibility, aspiring candidates are needed to have attained a Bachelors degree in any of Physics, Biological Sciences, BAMS, BHMS, BPT and any other related discipline, with a minimum aggregate score of 50%.
Top Institutes offering this M.Sc. Biotechnology are:
University of Hyderabad-School of Life Sciences, University of Mumbai-Institute of Chemical Technology, National Dairy Research Institute 
Rajiv Gandhi Center for Biotechnology 
Lovely Professional University 
Delhi Technological University-Department of Biotechnology, Indian Institute of Technology-Department of Biochemical Engineering & Biotechnology, Delhi University
Banaras Hindu University
Jawaharlal Nehru University 
Aligarh Muslim University of Mumbai
VIT, BITS, JMI, Christ University.
The average tuition fee charged in India for the course ranges between INR 40,000 to 2 Lacs.
Admission to the course is based on the candidates performance in a relevant entrance exam such as JAM, GATE, JNU CEEB etc. Biotechnology is a research-oriented subject which combines the disciplines of Technology and Biology. M.Sc. Biotechnology Syllabus is designed in such a way that it enhances candidates knowledge about biotechnology and its related disciplines such as genetics, animal biotechnology, food technology, plant biotechnology, etc. 
The average annual salary offered for these positions varies between INR 2 and 9 Lacs annually.
Organizations such as Abbott Laboratories, Baxter, Bristol-Myers Squibb, Johnson & Johnson, Merck, Biocon, IFGL, Bioceramics Limited, Orbees medical, Invitrogen, GlaxoSmithKline, Reliance life sciences, CTS life sciences, Dr.Reddys labs, Cipla, Jubilant life sciences, Wockhardt, Torrent Pharma, Cadila Healthcare and Ranbaxy and Pfizer etc. hire such postgraduates
Such postgraduates are hired in capacities such as Sr. Associate Scientist, Research Biochemist, Sr. Regulatory Affairs Associate, Biotechnology Researcher, Associate Engineer, Quality Controller and Regional Manager and in industries such as Pharmaceuticals, Manufacturing, Biotechnology, Research Organizations, and FMCG besides colleges and universities as teachers.

YES you are eligible for MSc.

here is the eligibility criteria for the admission

B.Sc. (Minimum 3 years duration in any subjects)

B.V. Sc./B. Pharma with 60% marks (55% for SC/ST) 

 MBBS/BDS with atleast 55% marks (50% for SC/ST)