A composite nanostructure based on quasi-one-dimensional InP nanowires with an InAsP nanoinsert, grown on a Si(111) substrate by the method of molecular-beam epitaxy, and CdSe/ZnS zero-dimensional colloidal quantum dots is reported for the first time. The nonradiative resonance energy transfer between components of the hybrid nanostructure, namely, between the colloidal quantum dots and the nanoinsert, is experimentally confirmed.