Background: The COVID-19 outbreak has made funders, researchers and publishers agree to have research publications, as well as other research outputs, such as data, become openly available. In this extraordinary research context of the SARS CoV-2 pandemic, publishers are announcing that their coronavirus-related articles will be made immediately accessible in appropriate open repositories, like PubMed Central (PMC), agreeing upon funders’ and researchers’ instigation. Methods: This work uses Unpaywall, OpenRefine and PubMed to analyse the level of openness of the papers about COVID-19, published during the first quarter of 2020. It also analyses Open Access (OA) articles published about previous coronavirus (SARS CoV-1 and MERS CoV) as a means of comparison. Results: A total of 5,611 COVID-19-related articles were analysed from PubMed. This is a much higher amount for a period of 4 months compared to those found for SARS CoV-1 and MERS during the first year of their first outbreaks (337 and 125 articles, respectively). Regarding the levels of openness, 97.4% of the SARS CoV-2 papers are freely available; similar rates were found for the other coronaviruses. Deeper analysis showed that (i) 68.3% of articles belong to an undefined Bronze category; (ii) 72.1% of all OA papers don’t carry a specific license and in all cases where there is, half of them do not meet Open Access standards; (iii) there is a large proportion that present a copy in a repository, in most cases in PMC, where this trend is also observed. These patterns were found to be repeated in most frequent publishers: Elsevier, Springer and Wiley. Conclusions: Our results suggest that, although scientific production is much higher than during previous epidemics and is open, there is a caveat to this opening, characterized by the absence of fundamental elements and values on which Open Science is based, such as licensing.