We demonstrate experimentally that multiple four-wave mixing pumped by a dual-frequency input in a single-mode fiber is modulationally unstable. This collective type of instability leads, in the anomalous dispersion regime, to sideband growth around all-orders of four-wave mixing. This is in contrast with the normal dispersion regime where our measurements show that four-wave mixing exhibits no instability. Our conclusions are based on the first systematic mapping of the phenomenon as a function of the dual-pump input frequency separation.