Countries around the world are facing so many challenges to slow down the spread of the current SARS-CoV-2 virus. Vaccination is an effective way to combat this virus and prevent its spreading among individuals. Currently, there are more than 50 SARS-CoV-2 vaccine candidates in trials; only a few of them are already in use. The primary objective of this study is to analyse the public awareness and opinion toward the vaccination process and to develop a model that predicts the awareness and acceptability of SARS-CoV-2 vaccines in Saudi Arabia by analysing a dataset of Arabic tweets related to vaccination. Therefore, several machine learning models such as Support Vector Machine (SVM), Naïve Bayes (NB), and Logistic Regression (LR), sideways with the N-gram and Term Frequency-Inverse Document Frequency (TF-IDF) techniques for feature extraction and Long Short-Term Memory (LSTM) model used with word embedding. LR with unigram feature extraction has achieved the best accuracy, recall, and F1 score with scores of 0.76, 0.69, and 0.72, respectively. However, the best precision value of 0.80 was achieved using SVM with unigram and NB with bigram TF-IDF. However, the Long Short-Term Memory (LSTM) model outperformed the other models with an accuracy of 0.95, a precision of 0.96, a recall of 0.95, and an F1 score of 0.95. This model will help in gaining a complete idea of how receptive people are to the vaccine. Thus, the government will be able to find new ways and run more campaigns to raise awareness of the importance of the vaccine.