This paper proposes a new method of impact classification for a Structural Health Monitoring system through the use of Self-Attention, the central building block of the Transformer neural network. As a topical and highly promising neural network architecture, the Transformer has the potential to greatly improve the speed and robustness of impact detection. This paper investigates the suitability of this new network, confronting the advantages and disadvantages offered by the Transformer and a well-known and established neural network for impact detection, the Convolutional Neural Network (CNN). The comparison is undertaken on performance, scalability, and computational time. The inputs to the networks were created using a data transformation technique, which transforms the raw time series data collected from the network of piezoelectric sensors, installed on a composite panel, through the use of Fourier Transform. It is demonstrated that the Transformer method reduces the computational complexity of the impact detection significantly, while achieving excellent prediction results.