Instantaneous frequency measurement (IFM) of microwave signals is a fundamental functionality for applications ranging from electronic warfare to biomedical technology. Photonic techniques, and nonlinear optical interactions in particular, have the potential to broaden the frequency measurement range beyond the limits of electronic IFM systems. The key lies in efficiently harnessing optical mixing in an integrated nonlinear platform, with low losses. In this work, we exploit the low loss of a 35 cm long, thick silicon waveguide to efficiently harness Kerr nonlinearity and demonstrate, to the best of our knowledge, the first on-chip four-wave mixing-based IFM system. We achieve a large, 40 GHz measurement bandwidth and a record-low measurement error. Finally, we discuss the future prospect of integrating the whole IFM system on a silicon chip to enable the first reconfigurable, broadband IFM receiver with low latency.