Self-accelerating Airy beams, which are non-diffracting waves in the form of an Airy function that propagate in free space with constant acceleration, have received considerable attention in recent years. They are typically generated by manipulation of the phase front of the wave by means of specially-designed optical elements. Here we show that autofocusing, radially-symmetric Airy waves can form spontaneously as a laser beam propagates in a defocusing, nonlocal thermal nonlinear medium, inside a cylindrical channel with a reflective boundary. The effect of the boundary is to create a ring-shaped optical caustic, which converges to a focal point. We demonstrate this method experimentally and numerically, and present a semi-classical analytical model for the wave dynamics that shows that the self-generated, radially-symmetric wave is indeed a caustic with an Airy function profile. In the hydrodynamic representation of the nonlinear wave equation the ring-shaped caustic that we describe can be interpreted as a shock wave that forms as the “photonic fluid” bounces off the reflective boundary. These results suggest a very simple and accessible, yet mathematically accurate way to obtain autofocusing radially-symmetric Airy waves for various applications.