COVID-19 is an infectious illness that was initially identified toward the end of 2019 and was officially declared a pandemic in March 2020. Social media, particularly Twitter, is widely used by people and is considered the primary official tool affecting both the mental and physical health of the population, as it spreads information about the increasing number of positive cases or deaths through posted tweets. In recent years, natural language processing with deep learning has gained significant attention in the Sentiment Analysis domain. Sentiment Analysis is a useful way to interpret emotions from textual information. This work presents a comparative analysis of multi-class sentiment classification on a dataset of COVID-19-related Tweets, evaluating four machine learning classifiers, two deep learning models, and the pre-trained transformer based model BERT (Bidirectional Encoder Representations from Transformers). The results demonstrate that BERT outperforms all models attaining the highest performance metrics of 91.4%, 92.02%, 90.39%, and 89% for accuracy, precision, recall, and F1-score, respectively.