We analyze 99 Type Ia supernovae (SNeIa) observed in $H$ band (1.6--1.8 $mu$m) and find that SNeIa are intrinsically brighter in $H$-band with increasing host galaxy stellar mass. We find that SNeIa in galaxies more massive than $10^{10.44} M_{odot}$ are brighter in $H$ than SNeIa in less massive galaxies by $0.18 pm 0.05$ mag. The same set of SNeIa observed at optical wavelengths, after width-color-luminosity corrections, exhibit a $0.17 pm 0.05$ mag offset in the Hubble residuals. Removing two significant outliers reduces the step in $H$ band to $0.10 pm 0.04$ mag but has no effect on the optical mass step size. An analysis based on information criteria supports a step function with a break at $10^{10.44}~M_{odot}$ over a constant model with and without outliers for NIR and optical residuals. Less massive galaxies preferentially host more higher-stretch SNeIa, which are intrinsically brighter and bluer. It is only after correction for width-luminosity and color-luminosity relationships that SNeIa have brighter optical Hubble residuals in more massive galaxies. Thus the finding that SNeIa are intrinsically brighter in $H$ in more massive galaxies is a significant and opposite correlation as the intrinsic optical brightness. If dust and the treatment of intrinsic color variation were the main driver of the host galaxy mass correlation, we would not expect a correlation of brighter $H$-band SNeIa in more massive galaxies. The correlation we find thus suggests that dust is not the main explanation of the observed correlation between Hubble residual and host galaxy stellar mass.
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