The breaking of universal symmetry of electromagnetic field distribution in an anisotropic magnetoelectric material will give rise to nonzero vacuum momentum. This may lead to the transfer of momentum between the anisotropic quantum vacuum and the magnetoelectric material. Very recently, Feigel considered the quantum vacuum contribution to the momentum transfer effect ［Phys. Rev. Lett. 92 (2004) 020404］. An alternative approach is proposed based on the eigenvector equation of electromagnetic field to calculate the total mechanical contribution of all anisotropic quantum-vacuum modes to the material momentum. It is suggested that the said macroscopic mechanical effect of quantum vacuum on the anisotropic material can be detected by current technology (e.g. fiber optical sensor), which can measure nanoscale velocity. Physical mechanism of such quantum vacuum effects and potential applications are discussed.