Psychological stress has evolved as an important health concern across the globe. The vulnerability to stress and the ramifications of it have only worsened during the time of the COVID-19 pandemic. This necessitates a timely diagnosis of stress before the condition progresses to chronicity. In this context, the popularity of social media like Twitter, where large numbers of users share opinions without any social stigma, has emerged as a major resource of human opinions. This has led to an increased research interest in social media-based stress detection techniques. However, tweet-level stress detection techniques in the literature have left a void in leveraging the text information in tweets, especially the presence of sarcastic expressions in the tweet’s text content. To this end, a novel method called “Sarcasm-based Tweet-Level Stress Detection” (STSD) is proposed in this work with the modification of the logistic loss function to detect tweet-level stress by availing the information of sarcasm that exists in the tweet-content. The principle of the STSD model is to minimise the loss for non-sarcastic tweets while maximising the loss for sarcastic tweets. Furthermore, an extensive preprocessing and dimensionality reduction is performed using kernel principal component analysis (kernel PCA) to improve the performance by reducing the dimensions. The experimental results show that the proposed STSD model, when applied along with kernel PCA, records a significant improvement in accuracy by a minimum of 5.25% and a maximum of 9.19% over baseline models. Also, there is an increment in F1-score by at least 0.085 points and a maximum of 0.164 points when compared to the baseline models.