This paper presents material characteristics of a rigid magnetorheological (MR) foam that comprises polyurethane foam matrix and carbonyl iron particles (CIPs). Three different samples of MR foams are prepared by changing the concentration of CIPs (0, 35, and 70 g) in isotropic condition. In-depth characterization on the morphological properties, the field-dependent rheological behavior in terms of linear viscoelastic region and storage modulus, and the off-state sound absorption properties are then experimentally investigated. In the morphological observation, it is seen from the fluorescence micrographs that MR foam consists of open pore structure and the average size of the pores is decreased with the increment in CIPs content. In the rheological test of MR foam, it is identified that MR foam with the addition of 70 g of CIPs to the total of polyol and isocyanates (100 g) can enhance the storage modulus up to 112% compared with MR foam without CIPs. In the meantime, from the acoustic absorption test, it is shown that the maximum peaks of sound absorption coefficient (SAC) are shifted to the low frequency and the SAC is increased up to 229% due to the decrement in the pores size and increment in the storage modulus. The results achieved from this material characterization of MR foam provide useful guidelines for the development of new type smart materials associated with MR fluids and for the findings of appropriate applications which require controllability of both the stiffness and acoustic properties.