The coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been a significant health issue globally. Point-of-care (POC) testing that can offer a rapid and accurate diagnosis of SARS-CoV-2 at the early stage of infection is highly desirable to constrain this outbreak, especially in resource-limited settings. Herein, we present a G-quadruplex DNAzyme-based electrochemical assay that is integrated with a sequential flow controllable microfluidic device for the detection of SARS-CoV-2 cDNA. According to the detection principle, a pyrrolidinyl peptide nucleic acid probe is immobilized on a screen-printed graphene electrode for capturing SARS-CoV-2 DNA. The captured DNA subsequently hybridizes with another DNA probe that carries a G-quadruplex DNAzyme as the signaling unit. The G-quadruplex DNAzyme catalyzes the H2O2-mediated oxidation of hydroquinone to benzoquinone that can be detected using square-wave voltammetry to give a signal that corresponds to the target DNA concentration. The assay exhibited high selectivity for SARS-CoV-2 DNA and showed a good experimental detection limit at 30 pM. To enable automation, the DNAzyme-based assay was combined with a capillary-driven microfluidic device featuring a burst valve technology to allow sequential sample and reagent delivery as well as the DNA target hybridization and enzymatic reaction to be operated in a precisely controlled fashion. The developed microfluidic device was successfully applied for the detection of SARS-CoV-2 from nasopharyngeal swab samples. The results were in good agreement with the standard RT-PCR method and could be performed within 20 min. Thus, this platform offers desirable characteristics that make it an alternative POC tool for COVID-19 diagnosis.