Deep learning has transformed the field of data analysis by dramatically improving the state of the art in various classification and prediction tasks, especially in the area of computer vision. In biomedical engineering, a lot of new work is directed toward surface electromyography (sEMG)-based gesture recognition, often addressed as an image classification problem using convolutional neural networks (CNNs). In this paper, we utilize the Hilbert space-filling curve for the generation of image representations of sEMG signals, which allows the application of typical image processing pipelines such as CNNs on sequence data. The proposed method is evaluated on different state-of-the-art network architectures and yields a significant classification improvement over the approach without the Hilbert curve. Additionally, we develop a new network architecture (MSHilbNet) that takes advantage of multiple scales of an initial Hilbert curve representation and achieves equal performance with fewer convolutional layers.