Multispectral satellites that measure the reflected energy from the different regions on the Earth generate the multispectral (MS) images continuously. The following MS image for the same region can be acquired with respect to the satellite revisit period. The images captured at different times over the same region are called multitemporal images. Traditional compression methods generally benefit from spectral and spatial correlation within the MS image. However, there is also a temporal correlation between multitemporal images. To this end, we propose a novel generative adversarial network (GAN) based prediction method called MultiTempGAN for compression of multitemporal MS images. The proposed method defines a lightweight GAN-based model that learns to transform the reference image to the target image. Here, the generator parameters of MultiTempGAN are saved for the reconstruction purpose in the receiver system. Due to MultiTempGAN has a low number of parameters, it provides efficiency in multitemporal MS image compression. Experiments were carried out on three Sentinel-2 MS image pairs belonging to different geographical regions. We compared the proposed method with JPEG2000-based conventional compression methods and three deep learning methods in terms of signal-tonoise ratio, mean spectral angle, mean spectral correlation, and laplacian mean square error metrics. Additionally, we have also evaluated the change detection performances and visual maps of the methods. Experimental results demonstrate that MultiTempGAN not only achieves the best metric values among the other methods at high compression ratios but also presents convincing performances in change detection applications.