Fractional calculus is an extension of integer-order calculus, which can characterize complex dynamical systems with more accuracy. In recent years, significant progress has been made in the study of symmetries and conserved quantities within systems subject to unilateral constraints. Nevertheless, research that combines fractional calculus with unilateral constraints remains at an early stage. The primary objective of this paper is to systematically incorporate fractional calculus into the framework of Hamiltonian systems governed by unilateral constraints, and establish a coherent theoretical foundation for Noether symmetry and its associated conserved quantities in such fractionalorder Hamiltonian systems. To achieve this, we first derive the canonical equations for unilateral constraint Hamiltonian systems under both the Riemann-Liouville and the Caputo definitions of fractional derivatives, based on the fractional Hamilton principle and the formal definition of unilateral constraints. Subsequently, by introducing a one-parameter infinitesimal transformation group, the Noether symmetry for these systems corresponding to each type of fractional derivative is rigorously defined, and the corresponding determining equations are systematically established. Using these determining equations in conjunction with the system's canonical equations allows for the explicit derivation of the Noether conserved quantities. Finally, the results of the paper are verified through two examples and numerical simulations.