Topological materials are of interest to both fundamental science and advanced technologies because topological states are robust with respect to perturbations and dissipation. Experimental detection of topological invariants is thus in great demand but remains extremely challenging. Ultrafast laser-matter interactions, and in particular high-harmonic generation, meanwhile, were proposed several years ago as tools to explore the structural and dynamical properties of various matter targets. Here we show that the high-harmonic emission signal produced by a circularly polarized laser contains signatures of topological phases and transitions in the paradigmatic Haldane model. In addition to clear shifts of the overall emissivity and harmonic cutoff, the high-harmonic emission shows a unique circular dichroism, which exhibits clear changes in behavior at the topological phase boundary. Our findings pave the way to understand fundamental questions about the ultrafast electron-hole pair dynamics in topological materials via nonlinear high-harmonic generation spectroscopy.