A highly sensitive absorption-based sensor based on folded split-ring metamaterial graphene resonators (FSRMGRs) is designed, and its biomedical application in terahertz (THz) spectrum is investigated. The sensor has a nearly perfect absorption with a spectral absorption coefficient of 99.75% at 4 THz, with a high Q-factor (average) of 13.76. The resonance peak frequency is sensitive to the refractive index (RI) of the test medium (analyte) and a fairly high sensitivity of 851 GHz/RIU has been obtained. The specifications of the sensor can be tuned by an external DC-bias voltage applied to the graphene layer. According to the obtained results, the developed absorber appears to be a good candidate bio-sensing applications.