We show that in the SU(2) Georgi-Glashow model, ’t Hooft–Polyakov monopoles are produced by a classical instability in magnetic fields above the Ambjørn-Olesen critical field, which coincides approximately with the field at which Schwinger pair production becomes unsuppressed. Below it, monopoles can be produced thermally, and we show that the rate is higher than for pointlike monopoles by calculating the sphaleron energy as a function of the magnetic field. The results can be applied to production of monopoles in heavy-ion collisions or in the early Universe.