The complex [Co(L)(H2O)4](NO3)2 of (E)-4-(2-(3-methyl-5-oxo-1-(pyridin-2-yl)-1H-pyrazol-4(5H)-ylidene)hydrazinyl)-N-(pyrimidin-2-yl)benzenesulfonamide (L) was synthesized via the self-assembly technique. Its molecular and supramolecular structures were analyzed using FTIR, elemental analyses, and single-crystal X-ray diffraction, as well as Hirshfeld calculations. This complex crystallized in the triclinic space group 𝑃1̲ with Z = 2. The crystallographic asymmetric unit comprised one complex cation and two nitrate counter anions. This complex had distorted octahedral geometry around the Co(II) ion. Numerous intermolecular interactions affecting the molecular packing of this complex were conformed using Hirshfeld investigations. The most significant contacts for the cationic inner sphere [Co(L)(H2O)4]2+ were O···H (38.8%), H···H (27.8%), and N···H (9.9%). On the other hand, the main interactions for the counter NO3¯ ions were the O···H (79.6 and 77.8%), O···N (8.0%), and O···C (9.1%). A high propensity for making interactions for each atom pair in the contacts O…H, N…C, N…H, and C…C was revealed by enrichment ratio values greater than 1. The antibacterial efficacy of the complex and the free ligand were assessed. The free ligand had higher antibacterial activity (MIC = 62.5–125 µg/mL) than the [Co(L)(H2O)4](NO3)2 complex (MIC ≥ 250 µg/mL) versus all the studied bacteria.