A leading nonlinear effect in magnonics is the interaction that splits a high-frequency magnon into two low-frequency magnons with conserved linear momentum. Here, we report experimental observation of nonlocal three-magnon scattering between spatially separated magnetic systems, viz. a CoFeB nanowire and a yttrium iron garnet (YIG) thin film. Above a certain threshold power of an applied microwave field, a CoFeB Kittel magnon splits into a pair of counterpropagating YIG magnons that induce voltage signals in Pt electrodes on each side, in excellent agreement with model calculations based on the interlayer dipolar interaction. The excited YIG magnon pairs reside mainly in the first excited (n=1) perpendicular standing spin-wave mode. With increasing power, the n=1 magnons successively scatter into nodeless (n=0) magnons through a four-magnon process. Our results demonstrate nonlocal detection of two separately propagating magnons emerging from one common source that may enable quantum entanglement between distant magnons for quantum information applications.