A highly sensitive ammonia gas sensor exploiting the gas sensing characteristics of tin oxide (SnO2) has been reported. The methodology of the sensor is based on the phenomenon of surface plasmon resonance (SPR) with a fiber-optic probe consisting of coatings of silver as a plasmonic material and SnO2 as the sensing layer. The sensing principle relies on the change in refractive index of SnO2 upon its reaction with ammonia gas. The capability of the sensor has been tested for a 10 to 100 ppm concentration range of ammonia gas. To enhance the sensitivity, probes with different thicknesses of SnO2 have been fabricated and characterized for ammonia sensing. It has been found that at a particular thickness the sensitivity is highest. The reason for the highest sensitivity at a particular thickness has been evinced theoretically. The electromagnetic field distribution for the multilayer structure of the probe reveals the enhancement of the evanescent field at the tin oxide-ammonia gas interface, which in turn manifests the highest shift in resonance wavelength at a particular thickness. The selectivity of the probe has been tested for various gases, and it has been found to be most accurate for the sensing of ammonia. A sensor utilizing optical fiber, the SPR technique, and metal oxide as sensing element combines the advantages of a miniaturized probe, online monitoring, and remote sensing on one hand and stability, high sensitivity and selectivity, ruggedness, and low cost on the other.