Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue1. They could be used for several quantum information processing tasks such as error correction2, preparation by measurement3 and one-way quantum computing4. Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them5, 6. Recent progress in manipulating microwave photons in superconducting circuits7, 8, 9 has increased demand for a QND detector that operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme that measures the number of photons inside a high-quality-factor microwave cavity on a chip. This scheme maps a photon number, n, onto a qubit state in a single-shot by means of qubit–photon logic gates. We verify the operation of the device for n=0 and 1 by analysing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors5, 8, 9, 10, 11 because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer.