This study introduces a dual-band plasmonic absorber designed for simultaneous sensing applications in the near-infrared (NIR) and mid-infrared (MIR) regions. The absorber, composed of silver nanostructures on a metal plate with a dielectric spacer, exhibits a combination of localized and gap surface plasmon resonances, resulting in two distinct absorption peaks in the theoretical analysis conducted using numerical simulations. The two absorption peaks are located in the NIR band (1366 nm) and the MIR band (2683 nm), with impressive absorption rates of 99.5% and 99.99%, respectively. Numerical simulations further validate the sensor’s high refractive index sensitivity of 1550 nm/RIU, enabling the detection of biomolecules, proteins, viruses, and various solutes in aqueous solutions. Along with the significant resonance shift, the absorber offers two working windows in distinct IR regions and the flexibility to select wavelengths in both bands simultaneously, thereby expanding its application range in environmental monitoring, medical diagnostics, and chemical sensing.