We propose a data-driven secure wireless communication scheme, in which the goal is to transmit a signal to a legitimate receiver with minimal distortion, while keeping some information about the signal private from an eavesdropping adversary. When the data distribution is known, the optimal trade-off between the reconstruction quality at the legitimate receiver and the leakage to the adversary can be characterised in the information theoretic asymptotic limit. In this paper, we assume that we do not know the data distribution, but instead have access to a dataset, and we are interested in the finite blocklength regime rather than the asymptotic limits. We propose a data-driven adversarially trained deep joint source-channel coding architecture, and demonstrate through experiments with CIFAR-10 dataset that it is possible to transmit to the legitimate receiver with minimal end-to-end distortion while concealing information on the image class from the adversary.