<p>When quasicrystal coatings are attached to substrates and subjected to local loads, the separation of the contact region edges is a common mechanical phenomenon, which makes receding contact a typical scenario that must be considered in the design and analysis of such structures. The frictionless receding contact problem between a one-dimensional hexagonal quasicrystal (QC) layer and an elastic substrate is investigated in this paper. By applying the Fourier integral transform, the plane problem is transformed into the first-kind Cauchy singular integral equation, where the unknowns are contact stress and half-length. By employing the Gauss–Chebyshev integration formula, the singular integral equation is discretized into a system of algebraic equations. An iterative algorithm is constructed to obtain contact length and stress that satisfy the force equilibrium condition. The numerical results discuss the influence of surface load length, phonon elastic constants, phason elastic constants, phonon–phason coupling coefficients, and substrate shear modulus on the contact behavior. The study demonstrates that reducing the phonon–phason coupling coefficient and the shear modulus of substrate can lower the peak contact stress, thereby helping to minimize contact damage to the greatest extent possible.</p>