High-efficiency single-photon detection in the microwave domain is a key enabling technology for various quantum applications. However, the extremely low energy of microwave photons presents a fundamental challenge, preventing direct photon-to-charge conversion as achieved in optical systems using semiconductors. Here, we demonstrate continuous microwave photon detection with an efficiency approaching 70% in the single-photon regime. We use a hybrid system comprising a gate-defined double quantum dot (DQD) charge qubit in a gallium arsenide/aluminum gallium arsenide heterostructure, coupled to a high-impedance Josephson junction array cavity. We systematically optimize the hybrid architecture to maximize the detection efficiency by leveraging strong charge-photon coupling, tunable DQD tunnel rates, and the frequency tunability of both subsystems. The system efficiency is characterized over a frequency range of 3 to 5.2 gigahertz. Our results establish semiconductor-based cavity–quantum electrodynamics architectures as a scalable and versatile platform for efficient microwave photon detection, opening promising avenues for quantum microwave optics and quantum information technologies.