A new Zn(II)-based coordination polymer (1) comprising the Schiff base ligand obtained by the condensation of 5-aminosalicylic acid and salicylaldehyde has been synthesized. This newly synthesized compound has been characterized by analytical and spectroscopic methods, and finally, by single-crystal X-ray diffraction technique in this study. The X-ray analysis reveals a distorted tetrahedral environment around the central Zn(II) center. This compound has been used as a sensitive and selective fluorescent sensor for acetone and Ag+ cations. The photoluminescence measurements indicate that in the presence of acetone, the emission intensity of 1 displays quenching at room temperature. However, other organic solvents caused meagre changes in the emission intensity of 1. Additionally, the fluorescence intensity of 1 has been examined in the presence of different ketones viz. cyclohexanone, 4-heptanone, and 5-nonanone, to assess the interaction between the C=O group of the ketones and the molecular framework of 1. Moreover, 1 displays a selective recognition of Ag+ in the aqueous medium by an enhancement in its fluorescence intensity, representing its high sensitivity for the detection of Ag+ ions in a water sample. Additionally, 1 displays the selective adsorption of cationic dyes (methylene blue and rhodamine B). Hence, 1 showcases its potential as an excellent luminescent probe to detect acetone, other ketones, and Ag+ with an exceptional selectivity, and displaying a selective adsorption of cationic dye molecules.