We study the light-matter coupling of microcavity photons and an interband transition in a one-dimensional (1D) nanowire. Due to the Van Hove singularity in the density of states, resulting in a resonant character of the absorption line, the achievement of strong coupling becomes possible even without the formation of a bound state of an electron and a hole. The calculated absorption in the system and corresponding energy spectrum reveal anticrossing behavior characteristic of the formation of polariton modes. In contrast to the case of conventional exciton polaritons, the formation of 1D Van Hove polaritons will not be restricted to low temperatures and can be realized in any system with a singularity in the density of states.