The novel coronavirus disease (COVID-19) pandemic is provoking a prevalent consequence on mental health because of less interaction among people, economic collapse, negativity, fear of losing jobs, and death of the near and dear ones. To express their mental state, people often are using social media as one of the preferred means. Due to reduced outdoor activities, people are spending more time on social media than usual and expressing their emotion of anxiety, fear, and depression. On a daily basis, about 2.5 quintillion bytes of data are generated on social media, analyzing this big data can become an excellent means to evaluate the effect of COVID-19 on mental health. In this work, we have analyzed data from Twitter microblog (tweets) to find out the effect of COVID-19 on peoples mental health with a special focus on depression. We propose a novel pipeline, based on recurrent neural network (in the form of long-short term memory or LSTM) and convolutional neural network, capable of identifying depressive tweets with an accuracy of 99.42%. Preprocessed using various natural language processing techniques, the aim was to find out depressive emotion from these tweets. Analyzing over 571 thousand tweets posted between October 2019 and May 2020 by 482 users, a significant rise in depressing tweets was observed between February and May of 2020, which indicates as an impact of the long ongoing COVID-19 pandemic situation.