Biosensors based on graphene field-effect transistors (G-FET) for detecting COVID-19 spike S protein and its receptor ACE2 were reported. The graphene, directly synthesized on SiO2/Si substrate by microwave plasma-enhanced chemical vapor deposition (MW-PECVD), was used for FET biosensor fabrication. The commercial graphene, CVD-grown on a copper substrate and subsequently transferred onto a glass substrate, was applied for comparison purposes. The graphene structure and surface morphology were studied by Raman scattering spectroscopy and atomic force microscope. Graphene surfaces were functionalized by an aromatic molecule PBASE (1-pyrenebutanoic acid succinimidyl ester), and subsequent immobilization of the receptor angiotensin-converting enzyme 2 (ACE2) was performed. A microfluidic system was developed, and transfer curves of liquid-gated FET were measured after each graphene surface modification procedure to investigate ACE2 immobilization by varying its concentration and subsequent spike S protein detection. The directly synthesized graphene FET sensitivity to the receptor ACE2, evaluated in terms of the Dirac voltage shift, exceeded the sensitivity of the transferred commercial graphene-based FET. The concentration of the spike S protein was detected in the range of 10 ag/mL up to 10 μg/mL by using a developed microfluidic system and measuring the transfer characteristics of the liquid-gated G-FETs. It was found that the shift of the Dirac voltage depends on the spike S concentration and was 27 mV with saturation at 10 pg/mL for directly synthesized G-FET biosensor, while for transferred G-FET, the maximal shift of 70 mV was obtained at 10 μg/mL with a tendency of saturation at 10 ng/mL. The detection limit as low as 10 ag/mL was achieved for both G-FETs. The sensitivity of the biosensors at spike S concentration of 10 pg/mL measured as relative current change at a constant gate voltage corresponding to the highest transconductance of the G-FETs was found at 5.6% and 8.8% for directly synthesized and transferred graphene biosensors, respectively. Thus, MW-PECVD-synthesized graphene-based biosensor demonstrating high sensitivity and low detection limit has excellent potential for applications in COVID-19 diagnostics.