Superconducting qubits demonstrate good perspectives as scalable blocks for quantum information processing. These systems can be individually readout, addressed, and controlled, making them some of the most attractive thin-film qubits. Quantum measurements should be performed in order to readout the final state of flux qubits. To observe the dynamics of such systems, one requires a fast magnetometer with exceptional sensitivity and low back-action. We address the problem of reducing the back-action of an RF SQUID readout circuit, which may significantly destroy a Josephson flux qubit in the case of the circuits integration. The main sources of such back-action in conventional RF SQUID and DC SQUID circuits are low-ohmic shunting resistors ensuring high damping. The advantage of flux qubits is the presence of an optimal bias point at which, in the first-order approximation, the device is immune to fluctuations in readout and control lines. Nonetheless, even such systems have characteristics limited by a second-order dissipation. The dissipation can be eliminated by using an “ideal parametric readout” based on an RF SQUID acting in non-hysteretic adiabatic mode. In this paper, we propose an RF SQUID in a non-hysteretic regime as a fast, sensitive, and scalable readout system with low back-action for measurements of a single MW photon counter based on a flux qubit.