The main purpose of this paper is to study non-commutative ternary Nambu-Poisson algebras and their Homtype version. We provide construction results dealing with tensor product and direct sums of two (non- commutative) ternary (Hom-) Nambu-Poisson algebras. Moreover, we explore twisting principle of (non-commutative) ternary Nambu-Poisson algebras along with algebra morphism that lead to construct (non-commutative) ternary Hom- Nambu-Poisson algebras. Furthermore, we provide examples and a 3-dimensional classification of non-commutative ternary Nambu-Poisson algebras.