Summary: The purpose of this paper is to characterize the set of pointwise multipliers on \(\text{bmo}_{\phi,p}(X)\), which is a function space defined using the mean oscillation in \(L^p\)-sense \((1\leq p<\infty)\) and a weight function \(\phi(x, r):X\times \mathbb{R}_+\to\mathbb{R}_+\). S. Janson [Ark. Mat. 14, 189-196 (1976; Zbl 0341.43005)] has characterized pointwise multipliers on \(\text{bmo}_\phi(\mathbb{T}^n)\) on the \(n\)-dimensional torus \(\mathbb{T}^n\) for a weight function \(\phi(r):\mathbb{R}_+\to \mathbb{R}_+\). We [E. Nakai, Stud. Math. 105, No. 2, 105-119 (1993; Zbl 0812.42008); E. Nakai and K. Yabuta, J. Math. Soc. Jap. 37, 207-218 (1985; Zbl 0563.42013)] have extended his result to the case of the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\). In this paper, we show that a similar characterization holds on the space of homogeneous type in the sense of Coifman-Weiss.