Pointing towards a girl, Vipin says, "This girl is the daughter of the only child of my father." What is the relation of Vipin's wife Parvathy to that girl?

Let's break down the statement made by Vipin step-by-step:
1. "The only child of my father" $⟹$ Since Vipin is speaking, his father's only child is Vipin himself.
2. "Daughter of the only child of my father" $⟹$ Daughter of Vipin.

So, the girl is Vipin's daughter.
Therefore, Vipin's wife, Parvathy, will be the Mother of that girl.