Synthesis of a new (E)-N1-((9-ethyl-9H-carbazol-3-yl)methylene)-5-nitrobenzene-1,2-diamine as a fluorescent chemosensor for selective detection of Fe$^{3+}$ ion over a number of other metal ions is described. The method for the synthesis of the carbazole Schiff base was based on the condensation of carbazole-3-carbaldehyde with 4-nitro-o-phenyldiamine in dimethylformamide in a moderate yield. The structure of the final compound was characterized by $^{1}$H NMR, $^{13}$C NMR, IR, mass spectrometry, and single crystal X-ray diffraction. The final compound exhibited exceptional selective and sensitive turn-on fluorescence response to the Fe$^{3+}$ cation. The fluorescent intensity of the final compound was increased 20-fold and the stoichiometry ratio of the final compound to Fe$^{3+}$ was 1:1. The association constant and detection limit for Fe$^{3+}$ ion were predicted from fluorescence titrations as (1.36 $\pm $ 0.09).10$^{4}$ M$^{-1}$ and 1.0 to 6.0 $\mu $M, respectively. The photophysical behavior of the compound was further explored by DFT methods. The predicted UV-Vis spectrum by TDDFT calculations was compared to the observed absorption spectrum of the targeted compound.