COVID-19 has dramatically affected various aspects of human society with worldwide repercussions. Firstly, a serious public health issue has been generated, resulting in millions of deaths. Also, the global economy, social coexistence, psychological status, mental health, and the human-environment relationship/dynamics have been seriously affected. Indeed, abrupt changes in our daily lives have been enforced, starting with a mandatory quarantine and the application of biosafety measures. Due to the magnitude of these effects, research efforts from different fields were rapidly concentrated around the current pandemic to mitigate its impact. Among these fields, Artificial Intelligence (AI) and Deep Learning (DL) have supported many research papers to help combat COVID-19. The present work addresses a bibliometric analysis of this scholarly production during 2020. Specifically, we analyse quantitative and qualitative indicators that give us insights into the factors that have allowed papers to reach a significant impact on traditional metrics and alternative ones registered in social networks, digital mainstream media, and public policy documents. In this regard, we study the correlations between these different metrics and attributes. Finally, we analyze how the last DL advances have been exploited in the context of the COVID-19 situation.