Biotic and abiotic plant stress (e.g., frost, fungi, diseases) can significantly impact crop production. It is thus essential to detect such stress at an early stage before visual symptoms and damage become apparent. To this end, this paper proposes a novel deep learning method, called Spectral Convolution and Channel Attention Network (SC-CAN), which exploits the difference in spectral responses of healthy and stressed crops. The proposed SC-CAN method comprises two main modules: (i) a spectral convolution module, which consists of dilated causal convolutional layers stacked in a residual manner to capture the spectral features; (ii) a channel attention module, which consists of a global pooling layer and fully connected layers that compute inter-relationship between feature map channels before scaling them based on their importance level (attention score). Unlike standard convolution, which focuses on learning local features, the dilated convolution layers can learn both local and global features. These layers also have long receptive fields, making them suitable for capturing long dependency patterns in hyperspectral data. However, because not all feature maps produced by the dilated convolutional layers are important, we propose a channel attention module that weights the feature maps according to their importance level. We used SC-CAN to classify salt stress (i.e., abiotic stress) on four datasets (Chinese Spring (CS), Aegilops columnaris (co(CS)), Ae. speltoides auchery (sp(CS)), and Kharchia datasets) and Fusarium head blight disease (i.e., biotic stress) on Fusarium dataset. Reported experimental results show that the proposed method outperforms existing state-of-the-art techniques with an overall accuracy of 83.08%, 88.90%, 82.44%, 82.10%, and 82.78% on CS, co(CS), sp(CS), Kharchia, and Fusarium datasets, respectively.