to be well-above error correction thresholds. In superconducting quantum computers, measurement of the qubit state remains the lowest-fidelity operation. For the transmon, a prototypical superconducting qubit, measurement is carried out by scattering a microwave tone off the qubit. Conventionally, the frequency of this tone is of the same order as the transmon frequency. The measurement fidelity in this approach is limited by multi-excitation resonances in the transmon spectrum which are activated at high readout power. These resonances excite the qubit outside of the computational basis, violating the desired quantum non-demolition character of the measurement. Here, we find that strongly detuning the readout frequency from that of the transmon exponentially suppresses the strength of spurious multi-excitation resonances. By increasing the readout frequency up to twelve times the transmon frequency, we achieve a quantum non-demolition measurement fidelity of 99.93% with a residual probability of leakage to non-computational states of only 0.02%.