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Stress-induced perturbation of the antiferromagnetic long-range order in epitaxially grown Cr2O3 thin films gives rise to pronounced piezomagnetism and a significant reduction of the antiferromagnetic ordering temperature. The temperature dependence of the piezomagnetic moment measured by superconducting quantum interference device magnetometry reveals a power law behaviour with a critical exponent 2B=0.66 in accordance with the Ising anisotropy of a three-dimensional system. The observed shift of the Neel temperature allows estimating the internal lateral stress which is in excellent agreement with an independent estimate based on the elastic properties of Cr2O3 and the lattice mismatch at the interface between the sapphire substrate and the isostructural (111) Cr2O3 thin film. The isothermal freezing field dependence of the piezomoment is interpreted in terms of Zeeman energy arguments. Implications of the piezomagnetic effects for spintronic devices and the investigation of the piezomagnetoelectric effect are briefly discussed.