This work presents the generation of an Airy beam by a leaky-wave structure (LWS) designed from a substrate-integrated waveguide (SIW) with dimension-varying slots. The Airy beam is radiated by judiciously designing the length of the slots to modulate the phase distribution. Compared to Airy beams generated by phased array antennas or metasurfaces, no complex feeding network associated with phase shifters and no space-wave illumination is required, thus allowing one to reach a low-profile structure. The features of the generated Airy beam are verified by experimental measurements performed on the LWS operating in the microwave domain. The parabolic path as well as the self-accelerating mainlobe of the Airy beam is validated in a frequency band spanning from 7.5 GHz to 8 GHz. The proposed low-profile Airy beam generator can be readily applied to wireless near-field communications for applications related to wireless power transfer, radio frequency identification, and the Internet of Things.