We describe optical bistability in monolithically integrated, curved-mirror Fabry-Perot microcavities. The cavities were fabricated by controlled formation of circular delamination buckles within sputtered Si/SiO(2) multilayers. The dominant source of the bistability is heating due to residual absorption in the mirror layers, which leads to out-of-plane deflection of the buckled mirror. Hysteresis occurs for submilliwatt input powers.