Recently, the destructive impact of wildfires has proliferated; for instance, the August Complex wildfire in 2020 burned around 4% of California's landmass. This has caused increased economic damage and risk to human life. Additionally, climate change is anticipated to increase the severity of wildfires, making it imperative for accurate and efficient detection of wildfires. Machine Learning approaches allow for the automatic detection of wildfires, simultaneously prioritizing accuracy and efficiency, with minimal human intervention, thus decreasing the likelihood of increased economic damage and increasing firefighting responses. Convolutional Neural Networks (CNNs), while showing promise, are often limited by their inability to learn and capture deep spatial dependencies in satellite imagery tasks. In this paper, we propose FlameViT, a novel wildfire detection architecture based on Vision Transformers (ViT). Satellite images are more efficient to obtain and can cover wide areas prone to wildfires. We obtain a dataset of 40K+ satellite images from Canada's Open Government Portal, allowing FlameViT to be optimized to detect wildfires in satellite imagery. FlameViT uses Patch Extractor and Patch Embedding layers, followed by multiple Transformer Encoder layers with Multi-Head Self-Attention and feed-forward neural networks. FlameViT is hyperparameter-tuned and achieves a validation accuracy of 95%, outperforming various baselines in the wildfire detection task. FlameViT shows the power of Vision Transformers for wildfire detection tasks, and in conjunction with the use of satellite imagery, can provide an efficient and accurate way of detecting wildfires.