Plants are a source of food, medicines, fiber, fuel, etc. and are therefore crucial for our survival. Due to this, intensive care of plants should be done and it requires monitoring of their growth, size, yield, etc. However, manually monitoring such factors is often time-consuming and necessitates one to have in-depth knowledge of agriculture and plants. Thus, automatic systems for plant image analysis would be beneficial for practical and productive agriculture. Therefore, an automatic method is proposed for monitoring the growth of plants by first performing the segmentation of leaves in plant images and then calculating the segmented area. A deep learning-based architecture “U-Net” was used for the segmentation task. A benchmark dataset of 810 images was used to train and test the proposed deep learning network. The proposed model was trained within 3 hours and achieved a dice accuracy of 94.91% on the training set, 94.93% on the validation set, and 95.05% on the testing set. The proposed architecture was found very lightweight with fewer computations but achieved promising results as compared to other methods in the literature.