The narrowband meta-absorbers exhibit significantly enhanced electromagnetic confinement capabilities, showcasing broad application prospects in sensing fields. They can be applied for biomarker detection, chemical composition analysis, and monitoring of specific gas in the environment. In this work, we propose a 3D meta-absorber with an out-of-plane plasma mechanism based on a two-photon printing system. Compared to the conventional fabrication of a metal-insulator-metal 2D meta-absorber, the 3D absorber is composed of a metal layer and a resin layer from top to bottom; its manufacturing process is simpler, only including two-photon printing and magnetron sputtering deposition. A noticeable absorbing resonance appears at 0.3142 THz with perfect absorbance with a high Q-factor of 104.67. The theoretical sensitivity to the refractive index of the sensor reaches up to 172.5 GHz/RIU, with a figure of merit (FOM) of 19.56. In the experiments, it was validated as a meta-absorber with high sensitivity for doxycycline (DCH). As the DCH concentration increases from 0 to 4 mg/mL, the absorption intensity decreases around 49%, while the resonant frequency shift is around 70 GHz. It reflects the real-time residual content of DCH, and is potentially applied in trace antibiotic detection. The results showcase a perfect narrowband absorption capability with strong electromagnetic confinement in the terahertz spectrum, along with high-Q sensing characteristics of DCH. Compared to 2D metamaterials, the diversity of 3D metamaterial significantly expands, and introduces additional effects to provide greater flexibility in manipulating electromagnetic waves. The 3D device offers opportunities for the application of terahertz biochemical sensing.