The change has been forced due to a recent RBI mandate regarding recurring payments. The new mandate requires banks and financial institutions to implement an additional factor of authentication for such payments.
“[…] we have temporarily discontinued: (i) new member sign-ups for Amazon Prime Free Trial and (ii) new member sign-ups for Monthly Prime Membership until further notice. You can continue enjoying Prime membership benefits by renewing / signing up for the Three Month or Annual Prime Membership”reads the updated support page from Amazon.