According to the impact, infectious diseases are a critical risk for 2020 and the following years in the Global Risk Report. The realization of the Covid-19 virus set the pandemic as a crucial global risk for humans, the economy, and society. The main idea of this paper is to give insight into the global socio-economic consequences of the actual Covid-19 pandemic, with a specific view of the business of insurance and reinsurance companies, who are responding to the widening of the COVID-19 pandemic on multiple fronts—as claims payers, employers, and investment managers. Considering that both individuals and businesses face high costs and losses regarding disruption of travel, business interruption, and supply chains, many expect insurers to reimburse some of these costs and losses. Insurance companies are also significant investors in financial markets and will face losses due to equity and fixed income market losses regarding decreasing interest rates as an attempt of central banks worldwide to support their economies. The current crisis can also be considered the possibility of improving the insurance coverage related to pandemics by establishing (re)insurance schemes and pooling arrangements for other catastrophic risks and developing public-private partnerships to support the insurability of pandemic risk.