We report on the green preparation of one-dimensional metal coordination polymers by sonochemical approach. The spacer ligand 4,4′-bipyridine was ultrasonicated with chloride or acetate zinc salts to obtain [Zn(4,4′-bipy)Cl2]∞ and [Zn(4,4′-bipy)2(OAc)2]∞, respectively. Benign solvents such as ethanol and water were selected as reaction media, and the synthesis took place in a few minutes—a very short time compared to conventional methods where some days’ synthesis is required. X-ray powder diffraction, Fourier transform infrared spectroscopy, thermal analysis (thermogravimetric and differential scanning calorimetry), and CHN techniques investigated the influence of using different reaction solvents on the chemical, structural, and thermal properties of the final products. The 1D [Zn(4,4′-bipy)Cl2]∞ and [Zn(4,4′-bipy)2(OAc)2]∞ polymers, in agreement with the structures reported in the literature, were obtained in the form of nanocrystals with an average crystal size around 100 nm. As a proof of concept, a set of Gram-positive (Staphylococcus aureus) and Gram-negative bacteria (Klebsiella pneumoniae), and three yeast strains (Candida albicans, Candida krusei, Candida glabrata) were tested to evaluate the antimicrobial activity of the coordination polymers, following the Kirby–Bauer procedure and microplate dilution method. Thus, minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC), and minimal biofilm inhibitory concentration (MBIC) were evaluated. Except for Candida krusei, the compounds showed an appreciable antimicrobial and antibiofilm activity against these strains grown in the liquid medium.