In linear, lossless, time-invariant, and nonbiased acoustic systems, mode transitions are time reversible, consistent with Lorentz reciprocity and implying a strict symmetry in space-time for sound manipulation. Here, we overcome this fundamental limitation by implementing spatiotemporally modulated acoustic metamaterials that support nonreciprocal sound steering. Our mechanism relies on the coupling between an ultrathin membrane and external biasing electromagnetic fields, realizing programmable dynamic control of the acoustic impedance over a motionless and noiseless platform. The fast and flexible impedance modulation of our metamaterial imparts an effective unidirectional momentum in space-time to realize nonreciprocal transitions in k-ω space between different diffraction modes. On the basis of these principles, we demonstrate efficient nonreciprocal sound steering, showcasing unidirectional evanescent wave conversion and nonreciprocal upconversion focusing. More generally, our metamaterial platform offers opportunities for generation of nonreciprocal Bloch waves and extension to other domains, such as non-Hermitian topological and parity-time symmetric acoustics.