The Arabic language has undergone notable transformations over time, including the emergence of new vocabulary, the obsolescence of others, and shifts in word usage. This evolution is evident in the distinction between the classical and modern Arabic eras. Although historians and linguists have partitioned Arabic literature into multiple eras, relatively little research has explored the automatic classification of Arabic texts by time period, particularly beyond the domain of poetry. This paper addresses this gap by employing neural networks and deep learning techniques to automatically classify Arabic texts into distinct eras and periods. The proposed models are evaluated using two datasets derived from two publicly available corpora, covering texts from the pre-Islamic to the modern era. The study examines class setups ranging from binary to 15-class classification and considers both predefined historical eras and custom periodizations. Results range from F1-scores of 0.83 and 0.79 on the binary-era classification task using the OpenITI and APCD datasets, respectively, to 0.20 on the 15-era classification task using OpenITI and 0.18 on the 12-era classification task using APCD.