This paper proposes and tests a sequence-based modeling of deep learning (DL) for structural damage detection of floating offshore wind turbine (FOWT) blades using Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) neural networks. The complete framework was developed with four different designs of deep networks using unidirectional or bidirectional layers of LSTM and GRU networks. These neural networks, specifically developed to learn long-term and short-term dependencies within sequential information such as time-series data, are successfully trained with the sensor signals of damaged FOWT. The sensor data were simulated due to the limited availability of field data from damaged FOWTs using multiple computational methods previously validated with experimental tests. The simulations accounted for the damage scenarios with various intensities, locations, and damage shapes, totaling 1320 damage scenarios. Both the presence of damage and its location were detected up to an accuracy of 94.8% using the best performing model of the selected network when tested for independent signals. The K-fold cross-validation accuracy of the selected network is estimated to be 91.7%. The presence of damage itself was detected with an accuracy of 99.9% based on the cross-validation regardless of the damage location. Structural damage detection using deep learning is not restricted by the assumptions of the systems or the environmental conditions as the networks learn the system directly from the data. The framework can be applied to various types of civil and offshore structures. Furthermore, the sequence-based modeling enables engineers to harness the vast amounts of digital information to improve the safety of structures.