Exciton–polaritons are hybrids of light and matter formed at the strong coupling regime that exhibit interesting phenomena such as enhanced transport, long-range energy transfer, and nonlinear response. These properties make exciton–polaritons very promising quasiparticles for the development of novel optoelectronic applications in the so-called polaritonic devices. However, strong coupling is significantly damped by the absorption losses of the system, which lead to short-lived exciton–polaritons. Here, we demonstrate strong coupling between excitons in organic molecules and all-dielectric metasurfaces formed by arrays of polycrystalline silicon nanoparticles supporting Mie surface lattice resonances (MSLRs). Compared to Mie resonances in individual nanoparticles, MSLRs have extended mode volumes and much larger quality factors, which enables to achieve collective strong coupling with very large coupling strengths and Rabi energies. Moreover, the presence of electric and magnetic Mie resonances in high refractive index dielectric nanoparticles introduces a new degree of freedom in light–matter interaction. We show the hybridization of excitons with electric and magnetic MSLRs, to form exciton–polaritons with an electric or magnetic character. Our results demonstrate the potential of all-dielectric metasurfaces as novel platform to investigate and manipulate exciton–polaritons in low-loss polaritonic devices.