A planar microstrip terahertz (THz) bandstop filter has been proposed with defected ground structure with high insertion loss (S21) in a stopband of −25.8 dB at 1.436 THz. The parameters of the circuit model have been extracted from the EM simulation results. A dielectric substrate of Benzocyclobutene (BCB) is used to realize a compact bandstop filter using modified hexagonal dumbbell-shape defected ground structure (DB-DGS). In this paper, a defected ground structure topology is used in a λ/4, 50 Ω microstrip line at THz frequency range for compactness. No article has been reported on the microstrip line at terahertz frequency regime using DGS topology. The proposed filter can be used for sensing and detection in biomedical instruments in DNA testing. All the simulations/cosimulations are carried out using a full-wave EM simulator CST V.9 Microwave Studio, HFSS V.10, and Agilent Design Suite (ADS).