The application of matrix information geometry to radar signal processing and target detection is a new and interesting subject. Wake vortices are Doppler-spread after Fourier transform. The traditional Moving Target Detection (MTD) method cannot adequately accumulate returns power of the whole spectrum. Based on matrix information geometry, a matrix Constant False Alarm Rate (CFAR) detection method is proposed to improve the detection performance of a weak wake target. In this method, covariance matrices of the observed data can be constructed into a matrix manifold; compared with CFAR detection, the geodesic distance between the covariance matrix in the detection cell and the mean of covariance matrices in the secondary cell is regarded as the detection statistics. Using simulated wake vortices, the return data in background noise and the iterative estimation performance of Riemannian mean are analyzed; the geodesic distance of covariance matrices of target return and noise with varying signal-noise rate is analyzed; and the detection performance of the matrix CFAR and the conventional MTD method is compared.