The coronavirus COVID-19 pandemic is today’s major public health crisis, we have faced since the Second World War. The pandemic is spreading around the globe like a wave, and according to the World Health Organization’s recent report, the number of confirmed cases and deaths are rising rapidly. COVID-19 pandemic has created severe social, economic, and political crises, which in turn will leave long-lasting scars. One of the countermeasures against controlling coronavirus outbreak is specific, accurate, reliable, and rapid detection technique to identify infected patients. The availability and affordability of RT-PCR kits remains a major bottleneck in many countries, while handling COVID-19 outbreak effectively. Recent findings indicate that chest radiography anomalies can characterize patients with COVID-19 infection. In this study, Corona-Nidaan, a lightweight deep convolutional neural network (DCNN), is proposed to detect COVID-19, Pneumonia, and Normal cases from chest X-ray image analysis; without any human intervention. We introduce a simple minority class oversampling method for dealing with imbalanced dataset problem. The impact of transfer learning with pre-trained CNNs on chest X-ray based COVID-19 infection detection is also investigated. Experimental analysis shows that Corona-Nidaan model outperforms prior works and other pre-trained CNN based models. The model achieved 95% accuracy for three-class classification with 94% precision and recall for COVID-19 cases. While studying the performance of various pre-trained models, it is also found that VGG19 outperforms other pre-trained CNN models by achieving 93% accuracy with 87% recall and 93% precision for COVID-19 infection detection. The model is evaluated by screening the COVID-19 infected Indian Patient chest X-ray dataset with good accuracy.