The method and magnetic resonance apparatus for acquiring diffusion-weighted measurement data from a subject, (a) a diffusion module is activated that contains at least one diffusion gradient, and (b) an acquisition module is activated, which reads out measurement data by repetitions of RF excitation pulses, which are applied to the subject under examination, and phase-encoding gradients that are activated to spatially encode signals induced by the RF pulses. For at least one repetition, the RF excitation pulse are applied to the subject only if the phase-encoding gradients, activated for the spatially encoding signals, which are generated after the RF excitation pulse, have already reached their required strength. Steps (a) and (b) are repeated until all the required measurement data are acquired. The acquired measurement data are stored. A significant reduction in the noise level of DWI measurements is thereby achieved.