Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), a novel infectious member of the coronavirus family, has caused millions of cases of infection and deaths all over the world, and been declared a pandemic by the World Health Organization. Conventional laboratory-based diagnostic testing has faced extreme difficulties in meeting the overwhelming demand for testing worldwide, and this has brought about a pressing need for cost-effective rapid diagnosis. There has been a surge in the number of prototypes of diagnostic kits developed, although many of these have been found to be lacking in terms of their accuracy and sensitivity. One type of chip-based diagnostic platform is the aptamer-based biosensor. Aptamers are artificially synthesized oligonucleotides that are capable of specifically binding to a target antigen. As of now, some aptamers have been reported for SARS-CoV-2. Although many ultrasensitive aptasensors have been developed for viruses, few have been successfully adapted for SARS-CoV-2 detection. Our review discusses the recent developments in the domain of SARS-CoV-2 specific aptamer isolation, the design of electrochemical and optical aptasensors, and the implications of aptasensor-based COVID-19 diagnosis.