We report the detection of near-infrared (NIR) [Fe II] (1.644 $mu$m) and H$_{2}$ 1-0 S(1) (2.122 $mu$m) line features associated with Galactic supernova remnants (SNRs) in the first quadrant using two narrowband imaging surveys, UWIFE and UWISH2. Among the total of 79 SNRs fully covered by both surveys, we found 19 [Fe II]-emitting and 19 H$_{2}$-emitting SNRs, giving a detection rate of 24% for each. Eleven SNRs show both emission features. The detection rate of [Fe II] and H$_{2}$ peaks at the Galactic longitude ($l$) of $40^{circ}$-$50^{circ}$ and $30^{circ}$-$40^{circ}$, respectively, and gradually decreases toward smaller/larger $l$. Five out of the eleven SNRs emitting both emission lines clearly show an [Fe II]-H$_{2}$ reversal, where H$_{2}$ emission features are found outside the SNR boundary in [Fe II] emission. Our NIR spectroscopy shows that the H$_{2}$ emission originates from collisionally excited H$_{2}$ gas. The brightest SNR in both [Fe II] and H$_{2}$ emissions is W49B, contributing more than 70% and 50% of the total [Fe II] 1.644 $mu$m ($2.0 times 10^4$ L$_{odot}$) and H$_{2}$ 2.122 $mu$m ($1.2 times 10^3$ L$_{odot}$) luminosities of the detected SNRs. The total [Fe II] 1.644 $mu$m luminosity of our Galaxy is a few times smaller than that expected from the SN rate using the correlation found in nearby starburst galaxies. We discuss possible explanations for this.
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