Most of the FDA approved histone deacetylase inhibitors (HDACi) contain hydroxamate as the zinc binding group (ZBG). Hydroxamates form strong electrostatic metal chelation with divalent zinc present in HDAC. This strong zinc chelation leads to unwanted metabolic abnormalities. Therefore, the design of a non-hydroxamate moiety as a ZBG encourages medicinal chemistry researchers. Here, a series of nicotinamide derivatives have been designed and synthesized as HDACi. All compounds were tested for their inhibitory activities against pan HDACs (containing predominantly HDAC1 and HDAC2 isozymes) and against the HDAC3 isoform. Among these, compounds 6b and 6n showed comparable pan HDAC inhibitory activity (IC50 = 4.648 mM and IC50 = 5.481 mM, respectively) compared with BG45 (IC50 = 5.506 mM). Compound 6b exhibited the best potency against HDAC3 with IC50 = 0.694 mM. In addition, the anti-proliferative activity of the synthesized compounds 6a–s was evaluated against three different cancer cell lines including B16F10, MCF-7, and A549. Compound 6b displayed the highest antiproliferative potency (IC50 = 4.66 mM in B16F10 cell lines) and compounds 6b, 6c, 6h, 6i, 6l, 6m, and 6n exhibited higher cytotoxicity against all cell lines compared with the reference BG45. The selected potent compounds also displayed significant selectivity against cancer cell lines over normal human embryonic kidney (HEK-293) cell lines. The molecular modelling study displayed possible interactions between the most potent inhibitor 6b and HDAC3 active sites. Furthermore, the predicted in silico studies of all target compounds revealed acceptable physicochemical properties and pharmacokinetic parameters.