Individuals who suffer from suicidal ideation frequently express their views and ideas on social media. Thus, several studies found that people who are contemplating suicide can be identified by analyzing social media posts. However, finding and comprehending patterns of suicidal ideation represent a challenging task. Therefore, it is essential to develop a machine learning system for automated early detection of suicidal ideation or any abrupt changes in a user’s behavior by analyzing his or her posts on social media. In this paper, we propose a methodology based on experimental research for building a suicidal ideation detection system using publicly available Reddit datasets, word-embedding approaches, such as TF-IDF and Word2Vec, for text representation, and hybrid deep learning and machine learning algorithms for classification. A convolutional neural network and Bidirectional long short-term memory (CNN–BiLSTM) model and the machine learning XGBoost model were used to classify social posts as suicidal or non-suicidal using textual and LIWC-22-based features by conducting two experiments. To assess the models’ performance, we used the standard metrics of accuracy, precision, recall, and F1-scores. A comparison of the test results showed that when using textual features, the CNN–BiLSTM model outperformed the XGBoost model, achieving 95% suicidal ideation detection accuracy, compared with the latter’s 91.5% accuracy. Conversely, when using LIWC features, XGBoost showed better performance than CNN–BiLSTM.