We provide a formal proof for the indifferentiability of SKINNY-HASH internal function from a random oracle. SKINNY-HASH is a family of sponge-based hash functions that use functions (instead of permutations) as primitives, and it was selected as one of the second round candidates of the NIST lightweight cryptography competition. Its internal function is constructed from the tweakable block cipher SKINNY. The construction of the internal function is very simple and the designers claim n-bit security, where n is the block length of SKINNY. However, a formal security proof of this claim is not given in the original specification of SKINNY-HASH. In this paper, we formally prove that the internal function of SKINNY-HASH has n-bit security, i.e., it is indifferentiable from a random oracle up to O(2n) queries, substantiating the security claim of the designers.