India is ranked fifth in the world in terms of COVID-19 publications accounting for 6.7% of the total. About 60% of the COVID-19 publications in the year 2020 are from United States, China, UK, Italy, and India. We present a bibliometric analysis of the publication trends and citation structure along with the identification of major research clusters. By performing network analysis of authors, citations, institutions, keywords, and countries, we explore semantic associations by applying visualization techniques. Our study shows lead taken by the United States, China, UK, Italy, India in COVID-19 research may be attributed to the high prevalence of COVID-19 cases in those countries witnessing the first outbreak and also due to having access to COVID-19 data, access to labs for experimental trials, immediate funding, and overall support from the govt. agencies. A large number of publications and citations from India are due to co-authored publications with countries like the United States, UK, China, and Saudi Arabia. Findings show health sciences have the highest number of publications and citations, while physical sciences and social sciences and humanities counts were low. A large proportion of publications fall into the open-access category. With India as the focus, by comparing three major pandemics—SARS, MERS, COVID-19—from a bibliometrics perspective, we observe much broader involvement of authors from multiple countries for COVID-19 studies when compared to SARS and MERS. Finally, by applying bibliometric indicators, we see an increasing number of sustainable development-related studies from the COVID-19 domain, particularly concerning the topic of good health and well-being. This study allows for a deeper understanding of how the scholarly community from a populous country like India pursued research in the midst of a major pandemic which resulted in the closure of scientific institutions for an extended time.