There is no attribution for this quote that can be pinned down. It is said, in some form or another, all over the world, not just in India. After all, the mother is often the first person the baby is taught by. It’s historically been a mother’s job to be there and teach the child. This isn’t as true anymore because mothers work just as much as fathers do outside the home nowadays.
However, in India, many women still struggle to find work after having children. In India, it is as true now as 100 years ago that the mother is a child’s first teacher. Babies learn to speak, to walk, to think from those around them. If that’s the mother, then that’s the baby’s first teacher.