Periodic driving provides a platform to dynamically tailor quantum states of matter, yet its impact on symmetry-protected topological phases remains incompletely understood. Here, we demonstrate that periodic driving enables the realization of an odd-parity altermagnetic (AM) higher-order topological insulator (HOTI) phase in the Cr₂CH₂ monolayer. In equilibrium, Cr₂CH₂ is a 2D antiferromagnetic (AFM) HOTI protected by C₃ rotational symmetry, characterized by a symmetry indicator χ⁽³⁾ = {-2,1} and robust corner states. Under circularly polarized light (CPL), the system develops a f-wave altermagnetic state governed by the symmetry [C₂||3̄₀₀₁] with odd-parity spin splitting. Despite substantial Floquet-induced band renormalization, the C₃-protected corner states remain intact over a broad range of driving strengths, highlighting the altermagnetic higher-order topology under Floquet driving. As the light intensity increases, the system gradually evolves into an altermagnetic semimetallic state. These results establish a direct connection between magnetism and topology in a periodically driven AFM system, offering a route toward the control of coupled spin and topological transport.