Predicting fading channels is a classical problem with a vast array of applications, including as an enabler of artificial intelligence (AI)-based proactive resource allocation for cellular networks. Under the assumption that the fading channel follows a stationary complex Gaussian process, as for Rayleigh and Rician fading models, the optimal predictor is linear, and it can be directly computed from the Doppler spectrum via standard linear minimum mean squared error (LMMSE) estimation. However, in practice, the Doppler spectrum is unknown, and the predictor has only access to a limited time series of estimated channels. This paper proposes to leverage meta-learning in order to mitigate the requirements in terms of training data for channel fading prediction. Specifically, it first develops an offline low-complexity solution based on linear filtering via a meta-trained quadratic regularization. Then, an online method is proposed based on gradient descent and equilibrium propagation (EP). Numerical results demonstrate the advantages of the proposed approach, showing its capacity to approach the genie-aided LMMSE solution with a small number of training data points.