We introduce a detection scheme for the state of a qubit that is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the qubit and is used as its detector. Close to the fundamental resonator frequency, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the qubit state, these few-photon resonances are shifted to different driving frequencies. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced readout fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current qubit inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.