AbstractOptical orbital angular momentum (OAM) Hall effect requires the interaction between different angular momenta, which hosts great potential in the manipulation of light. Dozens of studies have revealed that this interaction depends on the materials that the waves pass through. Negative refraction has given rise to many exceptional phenomena in the past decades, which greatly inspires us to investigate the interaction between OAM and double negative index materials (DNMs). It is demonstrated that in‐plane optical vortex waves can exhibit transverse shift through DNM, and such a phenomenon is also called vortex Hall effect. From numerical calculations, a linear relationship is observed between the transverse shift and the topological charge l for a fixed wavelength. The transverse shift originates from the transition of the caustics of the vortex source through DNM. The general theory reported in this work can be applied in more than electromagnetic (EM) systems. Acoustic experiment is performed to support the proposed theory due to the equivalence between acoustic and EM systems. The vortex Hall effect is then observed experimentally utilizing acoustic space‐coiling metamaterials, which can be effectively regarded as DNM. This phenomenon will help to understand the superoscillations of the vortex source, as well as bring significant applications in on‐chip signal de‐multiplexing.