Communication technologies like voice over IP operate under constrained real-time conditions, with voice packets being subject to delays and losses from the network. In such cases, the packet loss concealment (PLC) algorithm reconstructs missing frames until a new real packet is received. Recently, autoregressive deep neural networks have been shown to surpass the quality of signal processing methods for PLC, specially for long-term predictions beyond 60 ms. In this work, we propose a non-autoregressive adversarial auto-encoder, named PLAAE, to perform real-time PLC in the waveform domain. PLAAE has a causal convolutional structure, and it learns in an auto-encoder fashion to reconstruct signals with gaps, with the help of an adversarial loss. During inference, it is able to predict smooth and coherent continuations of such gaps in a single feed-forward step, as opposed to autoregressive models. Our evaluation highlights the superiority of PLAAE over two classic PLCs and two deep autoregressive models in terms of spectral and intonation reconstruction, perceptual quality, and intelligibility.