The global challenges posed by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic have underscored the critical importance of innovative and efficient control systems for addressing future pandemics. The most effective way to control the pandemic is to rapidly suppress the spread of the virus through early detection using a rapid, accurate, and easy-to-use diagnostic platform. In biosensors that use bioprobes, the binding affinity of molecular recognition elements (MREs) is the primary factor determining the dynamic range of the sensing platform. Furthermore, the sensitivity relies mainly on bioprobe quality with sufficient functionality. This comprehensive review investigates aptamers and nanobodies recently developed as advanced MREs for SARS-CoV-2 diagnostic and therapeutic applications. These bioprobes might be integrated into organic bioelectronic materials and devices, with promising enhanced sensitivity and specificity. This review offers valuable insights into advancing biosensing technologies for infectious disease diagnosis and treatment using aptamers and nanobodies as new bioprobes.