The $JHK_S$ magnitudes of the red giant branch tip (TRGB) and the distance moduli of the nearby dwarf irregular galaxy IC 1613 have been determined from the near-infrared luminosity functions (LFs) of the resolved stars in the galaxy. Applying a Savitzky-Golay filtering, we derived the second derivatives of the LFs, and estimated the apparent magnitudes of the TRGB as $m_J;=;19.1$, $m_H;=;18.4$, and $m_{Ks};=;18.0$. The mean values of the theoretical absolute magnitudes of the TRGB were measured by using the Yonsei-Yale isochrones with a metallicity range of -2.1 < [Fe/H] < -0.5 and age of 12 Gyr. The derived values of near-infrared TRGB distance moduli for IC 1613 are (m - M) = $24.12{pm}0.25$, $24.20{pm}0.44$, and $24.00{pm}0.52$ for J, H, and $K_S$ bands, respectively.