Tobacco is an important economic crop in the southern part of China, e.g., Fujian Province. Detailed spatial information of tobacco planting is essential for a good agriculture plan and sustainable management of tobacco. Optical remote sensing images acquired in the Fujian region are heavily affected by cloud coverage due to a subtropical climate. In this study, we investigate the use of time series C-band Sentinel-1 (S1) SAR data to extract tobacco planting areas. We use a Long Short-Term Memory (LSTM) model to quantify the relations between tobacco’s phenological information and the time series of features extracted from S1 SAR data. More specifically, the VH polarization channel was used to create the time series of feature datasets. Experiments were conducted on the S1 SAR dataset acquired during the growth cycle of tobacco from 2019 to 2020 in Nanping, Fujian, China. To evaluate the effectiveness of the proposed method, we compared the extraction results with that of the conventional machine learning method, i.e., Light Gradient Boosting Machine (Light GBM). Results show that the tobacco areas extracted by the proposed LSTM method have an overall accuracy of 82.9%, based on validation samples derived from very high resolution remote sensing images and a field survey conducted in 2020. The obtained extraction accuracy is higher than that of the Light GBM method, i.e., 78.6%. We conclude that the proposed LSTM method has a high potential for mapping tobacco planting in (sub)tropical regions using time series of S1 SAR data, and can be used as an alternative method for mapping the planting of other crop types from remote sensing images.