Register accuracy is an important indicator for measuring the quality of multicolor gravure printing. However, the accuracy of the photoelectric sensor register error detection does not meet the register control requirements for light-colored printed electronic products. To address this issue, the authors propose a high-precision register error detection method based on machine vision for circular matrix color marks. First, image denoising is carried out based on the characteristics of circular matrix color marks. Then a combined coarse–fine detection method is employed, and an improved Canny operator is used to detect pixel-level edge points in color marks. The eight-neighborhood edge tracking is performed by connecting the edges through morphological dilation processing. Then, based on pixel-level edges, the Zernike moment method is used to obtain subpixel-level edge points. Finally, the least squares method is utilized to fit the color mark center based on subpixel edges, and the register errors in both horizontal and vertical directions are obtained based on the distances between each color mark and the reference color mark center. Experimental results show that the proposed register error detection method based on matrix color marks achieves an average register error of 0.026 pixels. This method not only enhances the accuracy of register error detection but also demonstrates stability against noise and varying lighting conditions, meeting the demand for register error detection in complex gravure printing equipment.