Single photon detection is a key resource for sensing at the quantum limit and the enabling technologyfor measurement-based quantum computing. Photon detection at optical frequencies relies on irreversiblephotoassisted ionization of various natural materials. However, microwave photons have energies 5 ordersof magnitude lower than optical photons, and are therefore ineffective at triggering measurable phenomenaat macroscopic scales. Here, we report the observation of a new type of interaction between a single two-level system (qubit) and a microwave resonator. These two quantum systems do not interact coherently;instead, they share a common dissipative mechanism to a cold bath: the qubit irreversibly switches to itsexcited state if and only if a photon enters the resonator. We have used this highly correlated dissipationmechanism to detect itinerant photons impinging on the resonator. This scheme does not require any priorknowledge of the photon waveform nor its arrival time, and dominant decoherence mechanisms do nottrigger spurious detection events (dark counts). We demonstrate a detection efficiency of 58% and a recordlow dark count rate of 1.4 per millisecond. This work establishes engineered nonlinear dissipation as a keyenabling resource for a new class of low-noise nonlinear microwave detectors.