This paper summarizes the arguments and counterarguments within the scientific discussion on the healthcare systems' transformations towards sustainability, considering COVID-19 pandemic. The paper aims to forecast changes in the healthcare sector's greenhouse gas emissions of the EU countries. For gaining that purpose, the authors carried out the study in the following logical sequence. Firstly, the bibliometric analysis was conducted based on 2313 publications indexed by Scopus database. The study sample consists of 1995 publications indexed by the keywords such as healthcare, green, carbon and sustainable; and 318 publications – green, carbon-free, covid, pandemic, coronavirus and health. The fields for search are titles, keywords and abstracts. The search was limited to the subject areas such as Social science; Environmental sciences; Business, Management and Accounting; Economics, Econometrics and Finance. The time framework is 2000-2020. The scientific background analysis stated the strong relationship between implementing green innovation in the healthcare system towards gaining sustainable development goals. The obtained results indicated that the COVID-19 requires the decisive green transformation in the economy. Thus, the forecast of greenhouse gas volume from the healthcare activity (human health and social work activities; human health activities; manufacture of basic pharmaceutical products and pharmaceutical preparations) until 2030 was conducted. The methodological tool of this research based on the Autoregressive Integrated Moving Average (ARIMA) model. The software EViews 11 was used to provide empirical calculation. This study involved data of the EU countries such as Hungary, Slovakia, Malta, Denmark and Portugal from 1995 to 2019. The base of data is the EU statistical service Eurostat. Based on the obtained results, the authors concluded that there are still disparities in the healthcare sectors of the EU-countries towards sustainability. Therefore, the authors highlighted the necessity to improve the EU countries' cohesion policy, which would allow decisively and quickly cooperate to find effective solutions towards developing resilience in the healthcare sector due to implementing green strategies. The authors emphasized that this study's obtained results could be the base for future investigations devoted to effective green solutions to minimize greenhouse gas emissions from the healthcare activity.