(1) Background: Society and public policy have been remained interwoven since the inception of the modern state. Public health policy has been one of the important elements of the public administration of the Government of India (GOI). In order to universalize healthcare facilities for all, the GOI has formulated and implemented the national health policy (NHP). The latest NHP (2017) has been focused on the “Health in All” approach. On the other hand, the ongoing pandemic COVID-19 had left critical impacts on India’s health, healthcare system, and human security. The paper’s main focus is to critically examine the existing healthcare facilities and the GOI’s response to combat the COVID-19 apropos the NHP 2017. The paper suggests policy options that can be adopted to prevent the further expansion of the pandemic and prepare the country for future health emergency-like situations. (2) Methods: Extensive literature search was done in various databases, such as Scopus, Web of Science, Medline/PubMed, and google scholar search engines to gather relevant information in the Indian context. (3) Results: Notwithstanding the several combatting steps on a war-footing level, COVID-19 has placed an extra burden over the already overstretched healthcare infrastructure. Consequently, infected cases and deaths have been growing exponentially, making India stand in second place among the top ten COVID-19-infected countries. (4) Conclusions: India needs to expand the public healthcare system and enhance the expenditure as per the set goals in NHP-17 and WHO standards. The private healthcare system has not been proved reliable during the emergency. Only the public health system is suitable for the country wherein the population’s substantial size is rural and poor.