In this article, we prove the integrality of $v$-adic multiple zeta values (MZVs). For any index $\mathfrak{s}\in\mathbb{N}^r$ and finite place $v\in A := \mathbb{F}\_q\[\theta]$, Chang Mishiba introduced notion MZVs $\zeta\_A(\mathfrak{s})\_v$, which is a function field analogue Furusho's $p$-adic MZVs. By estimating valuation show that $\zeta\_A(\mathfrak{s})\_v$ integer for almost all $v$. T...