The problem of end-to-end learning of a communication system using an autoencoder -- consisting of an encoder, channel, and decoder modeled using neural networks -- has recently been shown to be a promising approach. A challenge faced in the practical adoption of this learning approach is that under changing channel conditions (e.g. a wireless link), it requires frequent retraining of the autoencoder in order to maintain a low decoding error rate. Since retraining is both time consuming and requires a large number of samples, it becomes impractical when the channel distribution is changing quickly. We propose to address this problem using a fast and sample-efficient (few-shot) domain adaptation method that does not change the encoder and decoder networks. Different from conventional training-time unsupervised or semi-supervised domain adaptation, here we have a trained autoencoder from a source distribution, that we want to adapt (at test time) to a target distribution using only a small labeled dataset and no unlabeled data. Our method focuses on a Gaussian mixture density network based channel model, and formulates its adaptation based on class and component-conditional affine transformations. The learned affine transformations are used to design an optimal input transformation at the decoder to compensate for the distribution shift, and effectively present to the decoder inputs close to the source distribution. Experiments on a real mmWave FPGA setup as well as a number of simulated distribution changes common to the wireless setting demonstrate the effectiveness of our method at adaptation using very small number of target domain samples.