The global pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused a threat to public health and a worldwide crisis. This raised the need for quick, effective, and sensitive detection tools to prevent the rapid transmission rate of the infection. Therefore, this study aimed to develop an electrochemical impedance spectroscopy (EIS)-based aptasensor employing an interdigitated gold electrode (IDE) to detect SARS-CoV-2 Spike (S) glycoprotein and viral particles. This allowed us to sensitively detect SARS-CoV-2 S glycoprotein with a limit of detection (LOD) of 0.4 pg/mL in a buffer solution and to obtain a linear increase for concentrations between 0.2 to 0.8 pg/mL with high specificity. The proposed aptasensor also showed a good sensitivity towards the heat-inactivated SARS-CoV-2 variants in a buffer solution, where the Delta, Wuhan, and Alpha variants were captured at a viral titer of 6.45 ± 0.16 × 10 TCID/mL, 6.20 × 10 TCID/mL, and 5.32 ± 0.13 × 10 TCID/mL, respectively. Furthermore, the detection of SARS-CoV-2 performed in a spiked human nasal fluid provided an LOD of 6.45 ± 0.16 × 10 TCID/mL for the Delta variant in a 50 µL sample and a detection time of less than 25 min. Atomic force microscopy images complemented the EIS results in this study, revealing that the surface roughness of the IDE after each modification step increased, which indicates that the target was successfully captured. This label-free EIS-based aptasensor has promising potential for the rapid detection of SARS-CoV-2 in complex clinical samples.