Heterostructures from complex oxides allow one to combine various electronic and magnetic orders as to induce new quantum states. A prominent example is the coupling between superconducting and magnetic orders in multilayers from high-Tc cuprates and manganites. A key role is played here by the interfacial CuO2 layer whose distinct properties remain to be fully understood. Here, we study with resonant inelastic X-ray scattering (RIXS) the magnon excitations of this interfacial CuO2 layer. In particular, we show that the underlying antiferromagnetic exchange interaction at the interface is strongly suppressed to J ≈ 70 meV, as compared to J ≈ 130 meV for the CuO2 layers away from the interface. Moreover, we observe an anomalous momentum dependence of the intensity of the interfacial magnon mode and show that it suggests that the antiferromagnetic order is accompanied by a particular kind of orbital order that yields a so-called altermagnetic state. Such a two-dimensional altermagnet has recently been predicted to enable new spintronic applications and superconducting proximity effects.