The race to publish results during the outbreak of the new coronavirus (SARS-CoV-2) has highlighted the relevance of sharing data and research results more quickly and openly than the current scientific communication system, as well as the role of social media in this context. This paper aims to analyze the impact of open access on the production and dissemination of knowledge about COVID-19 in traditional scientific communication and on the social web. We analyzed 6,631 papers and reviews of PubMed and Scopus databases, published between January and April 2020, through bibliometric and altmetric indicators. The results showed that the volume of scientific open access publications related to COVID-19 increased by an average monthly rate of 166% in the period analyzed. The countries with the highest number of publications are those that had the most registered cases of COVID-19. In general, the scientific open access publications had greater attention from social media and more intense cooperation networks than compared to non-open access publications. The combination of bibliometric and altmetric indicators allowed us not only to characterize the evolution and diffusion of scientific production on COVID-19 but also to understand the relationship between the pandemic caused by the new coronavirus and the interaction of society around research products. Our findings reinforce the importance of open access practices to create and strengthen research collaboration networks and to stimulate publications on emerging themes of global interest