Noncollinear magnetism opens exciting possibilities to generate topological superconductivity. Here, we focus on helical and cycloidal magnetic textures in magnet-superconductor hybrid structures in a background magnetic field. We demonstrate that this system can enter a topological phase which can be understood as a set of parallel topological wires. We explore and confirm this idea in depth with three different approaches: a continuum model, a tight-binding model based on the magnetic unit cell, and exact diagonalization on a finite two-dimensional lattice. The key signature of this topological state is the presence of Majorana bound states at certain disclination defects in the magnetic texture. Based on the C2 symmetry imposed by the helical or cycloidal texture, we employ the theory of topological crystalline superconductors with rotation invariants to obtain the Majorana parity at disclinations. Furthermore, we consider a 90-deg helimagnet domain wall, which is formed by a string of alternating disclinations. We discuss how the resulting chain of disclination bound states hybridizes into two chiral modes with different velocities. ... mehrWe suggest that hybrid systems of chiral magnets and superconductors are capable of hosting Majorana modes in various spatial configurations with potentially far less nanoengineering than in, e.g., semiconductor wires.