The proposed satellite test of the equivalence principle (STEP) will detect possible violations of the weak equivalence principle by measuring relative accelerations between test masses of different composition with a precision of one part in 10^{18}. A serendipitous by-product of the experimental design is that the absolute or common-mode acceleration of the test masses is also measured to high precision as they oscillate along a common axis under the influence of restoring forces produced by the position sensor currents, which in drag-free mode lead to Newtonian accelerations as small as 10^{-14} g. This is deep inside the low-acceleration regime where modified Newtonian dynamics (MOND) diverges strongly from the Newtonian limit of general relativity. We show that MOND theories (including those based on the widely used "n family" of interpolating functions as well as the covariant tensor-vector-scalar formulation) predict an easily detectable increase in the frequency of oscillations of the STEP test masses if the strong equivalence principle holds. If it does not hold, MOND predicts a cumulative increase in oscillation amplitude which is also detectable. STEP thus provides a new and potentially decisive test of Newton's law of inertia, as well as the equivalence principle in both its strong and weak forms.