One of the biggest challenges in experimental quantum information is to sustain the fragile superposition state of a qubit(1). Long lifetimes can be achieved for material qubit carriers as memories(2), at least in principle, but not for propagating photons that are rapidly lost by absorption, diffraction or scattering(3). The loss problem can be mitigated with a nondestructive photonic qubit detector that heralds the photon without destroying the encoded qubit. Such a detector is envisioned to facilitate protocols in which distributed tasks depend on the successful dissemination of photonic qubits(4,5), improve loss-sensitive qubit measurements(6,7) and enable certain quantum key distribution attacks(8). Here we demonstrate such a detector based on a single atom in two crossed fibre-based optical resonators, one for qubit-insensitive atom-photon coupling and the other for atomic-state detection(9). We achieve a nondestructive detection efficiency upon qubit survival of 79 +/- 3 per cent and a photon survival probability of 31 +/- 1 per cent, and we preserve the qubit information with a fidelity of 96.2 +/- 0.3 per cent. To illustrate the potential of our detector, we show that it can, with the current parameters, improve the rate and fidelity of long-distance entanglement and quantum state distribution compared to previous methods, provide resource optimization via qubit amplification and enable detection-loophole-free Bell tests.