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Instantaneous microwave frequency estimation enables numerous essential applications in the commercial, defense, and civilian marketplace. The advancement of applications is hindered by the bottleneck in electronic-based frequency measurement systems including narrow bandwidth, high errors rate, and low dynamic range. Photonics-based frequency estimation approaches not only increase the operation frequency range and provide rapid measurement response, but also benefit from immunity to electromagnetic interference and enhancement in system adaptability. Despite the unique advantages offered by photonics-based frequency estimation approaches, it is challenging to obtain linear mapping between the unknown frequency and the measured optical characteristics due to the nonlinear response in electro-optical devices, which consequently results in degradation in measurement precision and a complex calibration relationship. Therefore, it is critical to mitigate the challenge to achieve dynamic, adaptive, and high-precision estimation of microwave frequency. To this end, this paper presents the design and demonstration of a high-precision photonic based instantaneous frequency estimation system driven by machine learning. A three-layer deep neural network is used to tackle device nonlinearity and system noise, resulting in absolute error of < 50 MHz and root mean square error of 1.1 MHz.