Hey!
Yes, you can surely apply for Masters of Science in Clinical Embryology if you fulfill the following criteria:

• The minimum eligibility criteria according to different universities. Usually, it is mentioned that you need to pass in your undergraduate degree.
• Your bachelor's should be in the field of biology. Students from B.A. courses and B.Sc. with biology(or related branches) not as one of the subjects are not eligible to apply.

The criteria differs in different institutions. If you are planning to study abroad, your CV will be one of the deciding factors on your admission. Your internships will matter there.
In India, most of the universities either take students on the basis of a common entrance or their own entrance examinations, followed by an interview.

Hope it helps!