Deep neural network (DNN)-based receivers offer a powerful alternative to classical model-based designs for wireless communication, especially in complex and nonlinear propagation environments. However, their adoption is challenged by the rapid variability of wireless channels, which makes pre-trained static DNN-based receivers ineffective, and by the latency and computational burden of online stochastic gradient descent (SGD)-based learning. In this work, we propose an online learning framework that enables rapid low-complexity adaptation of DNN-based receivers. Our approach is based on two main tenets. First, we cast online learning as Bayesian tracking in parameter space, enabling a single-step adaptation, which deviates from multi-epoch SGD . Second, we focus on modular DNN architectures that enable parallel, online, and localized variational Bayesian updates. Simulations with practical communication channels demonstrate that our proposed online learning framework can maintain a low error rate with markedly reduced update latency and increased robustness to channel dynamics as compared to traditional gradient descent based method.