We investigate current-driven magnetization dynamics in synthetic [Fe/Cr](10) multilayer antiferromagnets by using low-frequency voltage noise measurements. We observe suppression of the noise above a critical current density of about 2x10(5) A/cm(2). Theoretical estimates suggest that this effect may be attributed to current-induced motion of domain walls in the antiferromagnet. The observed critical current density is about one order of magnitude smaller than for ferromagnetic systems. Our results are relevant for applications of antiferromagnetic metal spintronics in, e.g., magnetic memory storage technology.