Single-photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an impedance-matched artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. Each signal photon deterministically induces a Raman transition in the Λ system and excites the qubit. The subsequent dispersive readout of the qubit produces a discrete ‘click’. We attain a high single-photon-detection efficiency of 0.66±0.06 with a low dark-count probability of 0.014±0.001 and a reset time of ∼400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.