When a strong laser pulse induces the ionization of an atom, momentum conservation dictates that the absorbed photons transfer their momentum to the electron and its parent ion. The sharing of the photon momentum between the two particles and its underlying mechanism in strong-field ionization, occurring when the bound electron tunnels through the barrier created by the superposition of the atomic potential and the electric laser field, are still debated in theory1–4 after 30 years of research. Corresponding experiments are very challenging due to the extremely small photon momentum and their precision has been too limited, so far, to ultimately resolve this debate5–8. By utilizing an experimental approach relying on two counter-propagating laser pulses, we present a detailed study of the effects of the photon momentum in strong-field ionization. The high precision of the method and the intrinsically known zero momentum allow us to unambiguously demonstrate the action of the light’s magnetic field on the electron while it is under the tunnel barrier, which has only been theoretically predicted so far1–3,9, thereby disproving opposing predictions5,10,11. Our results deepen the understanding of, for example, molecular imaging12,13 and time-resolved photoelectron holography14.