A measurement necessarily changes the quantum state being measured, a phenomenon known as back-action. Real measurements, however, almost always cause a much stronger back-action than is required by the laws of quantum mechanics. Quantum non-demolition measurements have been devised(1-6) that keep the additional back-action entirely within observables other than the one being measured. However, this back-action on other observables often imposes its own constraints. In particular, free-space optical detection methods for single atoms and ions (such as the shelving technique(7), a sensitive and well-developed method) inevitably require spontaneous scattering, even in the dispersive regime(8). This causes irreversible energy exchange (heating), which is a limitation in atom-based quantum information processing, where it obviates straightforward reuse of the qubit. No such energy exchange is required by quantum mechanics(9). Here we experimentally demonstrate optical detection of an atomic qubit with significantly less than one spontaneous scattering event. We measure the transmission and reflection of an optical cavity(10-13) containing the atom. In addition to the qubit detection itself, we quantitatively measure how much spontaneous scattering has occurred. This allows us to relate the information gained to the amount of spontaneous emission, and we obtain a detection error below 10 per cent while scattering less than 0.2 photons on average. Furthermore, we performa quantum Zeno-type experiment to quantify the measurement back-action, and find that every incident photon leads to an almost complete state collapse. Together, these results constitute a full experimental characterization of a quantum measurement in the 'energy exchange-free' regime below a single spontaneous emission event. Besides its fundamental interest, this approach could significantly simplify proposed neutral-atom quantum computation schemes(14), and may enable sensitive detection of molecules and atoms lacking closed transitions.