Direct observations over the past four centuries(1) show that the number of sunspots observed on the Sun's surface varies periodically, going through successive maxima and minima. Following sunspot cycle 23, the Sun went into a prolonged minimum characterized by a very weak polar magnetic field(2,3) and an unusually large number of days without sunspots(4). Sunspots are strongly magnetized regions(5) generated by a dynamo mechanism(6) that recreates the solar polar field mediated through plasma flows(7). Here we report results from kinematic dynamo simulations which demonstrate that a fast meridional flow in the first half of a cycle, followed by a slower flow in the second half, reproduces both characteristics of the minimum of sunspot cycle 23. Our model predicts that, in general, very deep minima are associated with weak polar fields. Sunspots govern the solar radiative energy(8,9) and radio flux, and, in conjunction with the polar field, modulate the solar wind, the heliospheric open flux and, consequently, the cosmic ray flux at Earth(3,10,11).