This paper proposes a CNN-based deep learning model that classifies Arabic poems based on its era, which is not reported before. To build this model, constructing a dataset is the first step, so we propose an updated Arabic Poetry Dataset (2020). We use FastText word embeddings, based on the full corpus of poems (unlabeled). Two classifiers were trained, namely, a supervised deep learning classifier and a FastText-based classifier. We conducted several experiments. First, we implemented a polarity classifier of poems to modern and non-modern eras, which achieved highest accuracy and F1-score of 0.913 and 0.914, respectively, using a deep learning model without frequent terms. In the second experiment, we categorized poems into three eras. The classifier reported an accuracy and F1-score of 0.875 each. Last, the classification of poems into five different eras achieved highest accuracy and F1-score of 0.801 and 0.796, respectively.