Building a system for morphological processing is a challenging task in morphologically complex languages like Arabic. Although there are some deep learning based models that achieve successful results, these models rely on a large amount of annotated data. Building such datasets, specially for some of the lower-resource Arabic dialects, is very difficult, time-consuming, and expensive. In addition, some parts of the annotated data do not contain useful information for training machine learning models. Active learning strategies allow the learner algorithm to select the most informative samples for annotation. There has been little research that focuses on applying active learning for morphological inflection and morphophonological processing. In this paper, we have proposed a deep active learning method for this task. Our experiments on Egyptian Arabic show that with only about 30% of annotated data, we achieve the same results as does the state-of-the-art model on the whole dataset.