Wave propagation phenomena observed in nature not only involve complex physics but widely varying environmental parameters and dynamical scales. Thus, it is challenging to construct generalized physical models which can work in a broad range of situations. In this article, we present the convolutional autoencoder recurrent network (CRAN) as a data-driven model for scalable and generalized learning of wave propagation phenomenon. The CRAN consists of a convolutional autoencoder for learning a low-dimensional system representation and a long short-term memory recurrent neural network for learning the system evolution in low-dimension. Here we show that the convolutional autoencoder significantly outperforms the dimension-reduction of complex wave propagation phenomena via projection-based methods as it can directly learn subspaces resembling wave characteristics. On the other hand, the projection-based modes are restricted to the Fourier subspace. Geometric priors of the convolutional autoencoder enabling selective scale separation of complex wave propagation dynamics further enhance its capacity to reduce high- dimensional wave propagation data. We also show that geometric priors like translation equivariance and invariance of the convolutional autoencoder enable generalized learning of low-dimensional maps. Thus, the composite CRAN model connecting the convolutional autoencoder with a long short-term memory network specially designed for autoregressive modeling can perform generalized wave propagation prediction over the desired time horizon. Numerical experiments showing 90% mean structural similarity index measure for out-of-training CRAN predictions compared to the true solutions, and less than 10% point-wise L1 error for most cases, validate such generalization claims. Also, the CRAN predictions show similar wave characteristic patterns to the target solutions indicating not only their generalization but also their kinematical consistency.