Hi Shivani, You can do both courses. You should go for M.Sc Biotechnology, M.Sc Biotechnology will increase the chances of employment and better career growth. You can do it from: The 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 
 University of Mumbai

yes you can opt for masters in microbiology or biotechnology after having bachelors in biotechnology from colleges like sharda university, JNU, amity and so on but it is advisable to go for specialised courses in bachelors too.

if you are determined to pursue the certain degree, you must be in the same field.

zoology is not specialized course and you'd be only stuck to animal physiology and anat and so on but the bachelors or BTech degree in biotech offers you an all round study in complete sense of science, bio-chem, phy and technology as well as computer. if you go for all such suddenly after studying animals for 3 years, it might hamper your performance.

kindly think about it clearly before applying.

thank you and all the best.