Bottom-up text detection methods play an important role in arbitrary-shape scene text detection but there are two restrictions preventing them from achieving their great potential, i.e., 1) the accumulation of false text segment detections, which affects subsequent processing, and 2) the difficulty of building reliable connections between text segments. Targeting these two problems, we propose a novel approach, named ``MorphText", to capture the regularity of texts by embedding deep morphology for arbitrary-shape text detection. Towards this end, two deep morphological modules are designed to regularize text segments and determine the linkage between them. First, a Deep Morphological Opening (DMOP) module is constructed to remove false text segment detections generated in the feature extraction process. Then, a Deep Morphological Closing (DMCL) module is proposed to allow text instances of various shapes to stretch their morphology along their most significant orientation while deriving their connections. Extensive experiments conducted on four challenging benchmark datasets (CTW1500, Total-Text, MSRA-TD500 and ICDAR2017) demonstrate that our proposed MorphText outperforms both top-down and bottom-up state-of-the-art arbitrary-shape scene text detection approaches.