Frustrated magnetism in face-centered-cubic (fcc) magnetic sublattices remains underexplored but holds considerable potential for exotic magnetic behavior. Here we report on the crystal structure and the magnetic and thermodynamic properties of the 𝐴-site-vacant hydroxide double perovskite MnSn⁡(OH)₆. Despite dominant antiferromagnetic interactions among Mn²⁺ moments, evidenced by a negative Curie-Weiss temperature, the lack of a sharp thermodynamic transition down to 350 mK implies the absence of long-range magnetic order. However, a broad hump in the specific heat at 1.6 K suggests short-range correlations. Neutron diffraction at low temperatures confirms the presence of three-dimensional antiferromagnetic correlations, manifested as diffuse magnetic scattering with a correlation length 𝜉 = 24.66 Å and magnetic propagation vectors 𝐤 = (½ ½ ½) and (0 0.625 0) at 20 mK.