The global sanitary crisis caused by the emergence of the respiratory virus SARS-CoV-2 and the COVID-19 outbreak has revealed the urgent need for rapid, accurate, and affordable diagnostic tests to broadly and massively monitor the population in order to properly manage and control the spread of the pandemic. Current diagnostic techniques essentially rely on polymerase chain reaction (PCR) tests, which provide the required sensitivity and specificity. However, its relatively long time-to-result, including sample transport to a specialized laboratory, delays massive detection. Rapid lateral flow tests (both antigen and serological tests) are a remarkable alternative for rapid point-of-care diagnostics, but they exhibit critical limitations as they do not always achieve the required sensitivity for reliable diagnostics and surveillance. Next-generation diagnostic tools capable of overcoming all the above limitations are in demand, and optical biosensors are an excellent option to surpass such critical issues. Label-free nanophotonic biosensors offer high sensitivity and operational robustness with an enormous potential for integration in compact autonomous devices to be delivered out-of-the-lab at the point-of-care (POC). Taking the current COVID-19 pandemic as a critical case scenario, we provide an overview of the diagnostic techniques for respiratory viruses and analyze how nanophotonic biosensors can contribute to improving such diagnostics. We review the ongoing published work using this biosensor technology for intact virus detection, nucleic acid detection or serological tests, and the key factors for bringing nanophotonic POC biosensors to accurate and effective COVID-19 diagnosis on the short term.