Metamaterial absorbers are used in the terahertz frequency regime as photo-detectors, as sensing elements, in imaging applications, etc. Narrowband absorbers, on account of their ultra-slender bandwidth within the terahertz frequency spectrum, show a significant shift in the absorption peak when an extrinsic entity relative to the absorber, like refractive index or temperature of the encircling medium, is altered. This property paves the path for the narrowband absorbers to be used as potential sensors to detect any alterations in the encircling medium. In this paper, a novel design of a terahertz metamaterial (MTM) absorber is proposed, which can sense the variations in the refractive index (RI) of the surrounding medium. The effective permeability of the structure is negative, while its permittivity is positive; thus, it is a μ-negative metamaterial. The layout involves a swastika-shaped design made of gold on top of a dielectric gallium arsenide (GaAs) substrate. The proposed absorber achieved a nearly perfect absorption of 99.65% at 2.905 terahertz (THz), resulting in a quality factor (Q-factor) of 145.25. The proposed design has a sensitivity of 2.12 THz/RIU over a range of varied refractive index from n = 1.00 to n = 1.05 with a step size of 0.005, thereby achieving a Figure of Merit (FoM) of 106. Furthermore, the sensor was found to have a polarization-insensitive characteristic. Considering its high sensitivity (S), the proposed sensor was further tested for gas sensing applications of harmful gases. As a case study, the sensor was used to detect chloroform. The proposed work can be the foundation for developing highly sensitive gas sensors.