Hello Pratima,
Firstly, I am not a F/T Business Analyst, although I have extensive experience in IT, some of it in a BA role.
The short answer to your question is ' No ' , you dont need to have product development experience to become a BA.
Many BA's I interacted with were for enhancements to existing products; perhaps one may surmise that Senior BA's would get more of the new product development work.
Essential skills would be good communication, business and technical skills; which seems evident from your educational background.
Perusing through this forum will give you the information you need, plus others more experienced than myself in BA could elaborate.
Cheers and Good Luck,
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