To study the excitation mechanism of near-infrared [Fe II] (a4F9/2-a4D7/2) emission at 1.644 μM in Seyfert and starburst galaxies, we compare the intensity of [Fe II] 1.644 μm with those of optical lines, [O I] λ6300, [S II] (λ6717 + λ6731), and [N II] λ6584, and we find a good correlation between the line ratio of [Fe II] 1.644 μm to hydrogen Brγ ([Fe II]/Brγ) and that of [O I] λ6300 to Hα ([O I]/Hα). No correlation between [Fe II]/Brγ and [N II]/Hα is found. The [O I] line is radiated from partly ionized hydrogen regions (hydrogen transition regions), while the [N II] line is radiated from fully ionized regions. Thus, it is concluded that the [Fe II] emission comes mainly from the transition regions in galactic nuclei and is excited by electron collisions. The observed correlation between [Fe II]/Brγ and [O I]/Hα can be explained by assuming that the [Fe II] and [O I] lines are radiated from the spatially similar regions. The [Fe II]/Brγ ratio is higher in active galactic nuclei (AGNs) than in starburst nuclei (SBNs). This property can be interpreted as being due to the presence of extended transition regions outside the fully ionized hydrogen zone in AGNs. The broad line widths of [Fe II] emission of NGC 1068 and NGC 4151 suggest that the [Fe II] emission comes from the narrow-line regions (NLRs). If this is the case, heating of gas due to nonthermal radiation plays an important role in the excitation of the [Fe II] emission in AGNs. On the other hand, in SBNs, the [Fe II] emission may not be due to photoionization by young OB stars but may be due to shock heating caused by starburst winds.