We discuss the large-distance approximation of the monopole-vortex complex soliton in a hierarchically broken gauge system, SU(N+1) \to SU(N) \to 1, in a color-flavor locked SU(N) symmetric vacuum. The ('t Hooft-Polyakov) monopole of the higher-mass-scale breaking appears as a point and acts as a source of the thin vortex generated by the lower-energy gauge symmetry breaking. The exact color-flavor diagonal symmetry of the bulk system is broken by each individual soliton, leading to nonAbelian orientational CP^{N-1} zeromodes propagating in the vortex worldsheet, well studied in the literature. As the vortex ends at the monopoles these fluctuating modes endow the monopoles with a local SU(N) charge. This phenomenon is studied by performing the duality transformation in the presence of the CP^{N-1} moduli space. The result is an effective action is a CP^{N-1} model defined on a finite-width worldstrip, in which the pointlike monopoles at the boundaries appear as the source and sink of the massless CP^{N-1} fluctuations. Our construction seems to explain the appearance of nonAbelian monopoles in various degenerate singularities of N=2 supersymmetric gauge theories.