Epitaxial strain modifies the physical properties of thin films deposited on single-crystal substrates. In a previous work, we demonstrated that in the case of La2/3Ca1/3MnO3 thin films the strain induced by the substrate can produce the segregation of a non-ferromagnetic layer (NFL) at the top surface of ferromagnetic epitaxial La2/3Ca1/3MnO3 for a critical value of the tetragonality τ, defined as τ = |c − a|a, of τC ≈ 0.024. Although preliminary analysis suggested its antiferromagnetic nature, to date a complete characterization of the magnetic state of such an NFL has not been performed. Here, we present a comprehensive magnetic characterization of the strain-induced segregated NFL. The field-cooled magnetic hysteresis loops exhibit an exchange bias mechanism below T ≈ 80 K, which is well below the Curie temperature of the ferromagnetic La2/3Ca1/3MnO3 layer. The exchange bias and coercive fields decay exponentially with temperature, which is commonly accepted to describe spin-glass (SG) behavior. The signatures of slow dynamics were confirmed by slow spin relaxation over a wide temperature regime. Low-energy muon spectroscopy experiments directly evidence the slowing down of the magnetic moments below ~100 K in the NFL. The experimental results indicate the SG nature of the NFL. This SG state can be understood within the context of the competing ferromagnetic and antiferromagnetic interactions of similar energies.