The single watermarking algorithm for medical images faced several inherent problems like lack of security. In this paper, a new geometrically invariant multiple zero-watermarking method is proposed to secure medical images. We proposed a novel set of multi-channels shifted Gegenbauer moments of fractional orders (FrMGMs). These moments are used to extract the geometrically invariant features from the color medical images. Then we construct a featured image of the original medical image using the magnitude of the selected precise FrMGMs moments. Finally, we applied a scrambling method to scramble the watermark image and then the exclusive OR operation to the images' feature and scrambled watermark to construct a zero-watermark. Experimental results proved that the proposed approach effectively provided better robustness to various standard attacks and outperformed the existing single-, dual-, & triple-zero-watermarking algorithms for medical images.