Twelve pyridazinones (T1–T12) containing the (2-fluorophenyl) piperazine moiety were designed, synthesized, and evaluated for monoamine oxidase (MAO) -A and -B inhibitory activities. T6 was found to be the most potent MAO-B inhibitor with an IC50 value of 0.013 µM, followed by T3 (IC50 = 0.039 µM). Inhibitory potency for MAO-B was more enhanced by meta bromo substitution (T6) than by para bromo substitution (T7). For para substitution, inhibitory potencies for MAO-B were as follows: -Cl (T3) > -N(CH3)2 (T12) > -OCH3 (T9) > Br (T7) > F (T5) > -CH3 (T11) > -H (T1). T6 and T3 efficiently inhibited MAO-A with IC50 values of 1.57 and 4.19 µM and had the highest selectivity indices (SIs) for MAO-B (120.8 and 107.4, respectively). T3 and T6 were found to be reversible and competitive inhibitors of MAO-B with Ki values of 0.014 and 0.0071, respectively. Moreover, T6 was less toxic to healthy fibroblast cells (L929) than T3. Molecular docking simulations with MAO binding sites returned higher docking scores for T6 and T3 with MAO-B than with MAO-A. These results suggest that T3 and T6 are selective, reversible, and competitive inhibitors of MAO-B and should be considered lead candidates for the treatment of neurodegenerative disorders like Alzheimer’s disease.