The separation and extraction of chrysin from active ingredients of natural products are of great significance, but the existing separation and extraction methods have certain drawbacks. Here, chrysin molecularly imprinted nanofiber membranes (MINMs) were prepared by means of electrospinning using chrysin as a template and polyvinyl alcohol and natural renewable resource rosin ester as membrane materials, which were used for the separation of active components in the natural product. The MINM was examined using Fourier transform infrared (FT-IR) spectroscopy, scanning electron microscopy (SEM), and thermogravimetric analysis (TGA). The adsorption performance, adsorption kinetics, adsorption selectivity, and reusability of the MINM were investigated in static adsorption experiments. The analysis results show that the MINM was successfully prepared with good morphology and thermal stability. The MINM has a good adsorption capacity for chrysin, showing fast adsorption kinetics, and the maximum adsorption capacity was 127.5 mg·g−1, conforming to the Langmuir isotherm model and pseudo-second-order kinetic model. In addition, the MINM exhibited good selectivity and excellent reusability. Therefore, the MINM proposed in this paper is a promising material for the adsorption and separation of chrysin.