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Quantum incompatibility, as an important quantum resource, is believed to play a key role in quantum information processing tasks. In order to detect this property, an entanglement-free incompatibility witness is proposed via constructing a combined quantum state discrimination task with prior-measurement and post-measurement information strategies. Here we experimentally implement the witness of the incompatibility of mutually unbiased measurements under different noise levels in a qutrit system. Moreover, we estimate the robustness of incompatibility using collected data. Our work paves the path for understanding quantum incompatibility and exploring the features of the quantum resource.