Polaritonic chemistry offers the possibility of modifying molecular properties and even influencing chemical reactivity through strong coupling between vibrational transitions and confined light modes in optical cavities. Despite considerable theoretical progress, and due to the complexity of the coupled light-matter system, the fundamental mechanism of how and if collective strong coupling can induce local changes in individual molecules is still unclear. We derive an analytical formulation of static polarizabilities within linear-response theory for molecules under strong coupling using the cavity Born–Oppenheimer Hartree–Fock ansatz. This ab-initio method consistently describes vibrational strong coupling and electron–photon interactions even for ensembles of molecules. For different types of molecular ensembles, we observed local changes in the polarizabilities and dipole moments that are induced by collective strong coupling. Furthermore, we used the polarizabilities to calculate vibro-polaritonic Raman spectra in the harmonic approximation. This allows us to comprehensively compare the effect of vibrational strong coupling on IR and Raman spectra on an equal footing.