Based on first-principles calculations combined with theoretical analysis, we identify a family of monolayer chromium-based group-IV chalcogenides as a new class of two-dimensional (2D) magnetic higher-order topological insulators (HOTIs). Specifically, the CrCX₃ (X= S, Se, Te) and CrSiS₃ monolayers are found to host conventional antiferromagnetic ground states with PT symmetry, whereas the Janus compounds Cr₂C₂S₃Se₃ and Cr₂Si₂S₃Se₃ exhibit altermagnetic ground states. We demonstrate that all these monolayer magnetic materials realize 2D HOTI phases, in which the nontrivial topology is protected by lattice C₃ rotational symmetry and manifests as zero-dimensional corner states carrying quantized fractional charges. Moreover, upon inclusion of spin-orbit coupling, these systems remain in the HOTI phase and continue to host robust corner-localized states, confirming the stability of their higher-order topological nature. Our results reveal an intrinsic connection between higher-order topology and magnetic order in 2D antiferromagnetic and altermagnetic systems, identifying chromium-based group-IV chalcogenide monolayers as promising platforms for exploring higher-order topological phases and their potential relevance for future topological and spintronic applications.