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A nematic transition preceding a long-range spin density wave antiferromagnetic phase is a common feature of many parent compounds of Fe-based superconductors. However, in the FeSe system with a nematic transition at Ts≈90 K, no evidence for long-range static magnetism is found down to very low temperatures. The lack of magnetism is a challenge for the theoretical description of FeSe. We investigated high-quality single crystals of FeSe using high-field (up to 9.5 T) muon spin rotation (μSR) measurements. The μSR Knight shift and the bulk susceptibility linearly scale at high temperatures but deviate from this behavior around T*∼10–20 K, where the Knight shift exhibits a kink. In the temperature range Ts≳T≳T*, the muon spin depolarization rate shows a quantum critical behavior Λ∝T−0.4. The observed critical scaling indicates that FeSe is in the vicinity of an itinerant antiferromagnetic quantum critical point. Below T* the quantum critical behavior breaks down. We argue that this breakdown is caused by a temperature-induced Lifschitz transition.