Coronaviruses constitute a family of virus that gives rise to respiratory diseases. Coronavirus disease 2019 is an infectious disease caused by a newly discovered coronavirus also termed as Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to its rapid spread, WHO has declared COVID-19 outbreak a pandemic on 11th March 2020. Reverse transcription-polymerase chain reaction (RT-PCR) test is popularly used worldwide for the detection of COVID-19. However, due to the high false-negative rate of RT-PCR test, chest X-ray (CXR) imaging is emerging as a feasible alternative for the detection of COVID-19. In this work, we propose a multiclass classification model COV-ELM, based on the extreme learning machine which classifies the CXR images into one of the three classes, namely COVID-19, normal, and pneumonia. The choice of ELM in this work has been motivated by its significantly short training time as compared to conventional gradient-based learning algorithms. After some preprocessing, we extract a pool of features based on texture and frequency. This pool of features serves as an input to the ELM and a 10-fold cross-validation method is employed to evaluate the proposed model. For experimentation, we use chest X-ray (CXR) images from three publicly available sources. The results of applying COV-ELM on test data are quite promising. The COV-ELM achieved a macro average F1-score of 0.95 and the overall sensitivity of 0.94 ± 0.02 at 95% confidence interval. When compared to state-of-the-art machine learning algorithms, the COV-ELM is found to outperform in a three-class classification scenario. The main advantage of COV-ELM is that its training time being quite low, as bigger and diverse datasets become available, it can be quickly retrained as compared to its gradient-based competitor models.