  We present a measurement of the Hubble constant ($H_0$) using type Ia
supernova (SNe Ia) in the near-infrared (NIR) from the recently updated sample
of SNe Ia in nearby galaxies with distances measured via Cepheid
period-luminosity relations by the SHOES project. We collect public
near-infrared photometry of up to 19 calibrator SNe Ia and further 57 SNe Ia in
the Hubble flow ($z>0.01$), and directly measure their peak magnitudes in the
$J$ and $H$ band by Gaussian processes and spline interpolation. Calibrator
peak magnitudes together with Cepheid-based distances are used to estimate the
average absolute magnitude in each band, while Hubble-flow SNe are used to
constrain the zero-point intercept of the magnitude-redshift relation. Our
baseline result of $H_0$ is $72.3\pm1.4$ (stat) $\pm1.4$ (syst) km s$^{-1}$
Mpc$^{-1}$ in the $J$ band and $72.3\pm1.3$ (stat) $\pm1.4$ (syst) km s$^{-1}$
Mpc$^{-1}$ in the $H$ band, where the systematic uncertainties include the
standard deviation of up to 21 variations of the analysis, the 0.7\% distance
scale systematic from SHOES Cepheid anchors, a photometric zeropoint
systematic, and a cosmic variance systematic. Our final measurement represents
a measurement with a precision of 2.8\% in both bands. The variant with the
largest change in $H_0$ is when limiting the sample to SNe from CSP and CfA
programmes, noteworthy because these are the best calibrated, yielding
$H_0\sim75$ km s$^{-1}$ Mpc$^{-1}$ in both bands. We demonstrate stretch and
reddening corrections are still useful in the NIR to standardize SN Ia NIR peak
magnitudes. Based on our results, in order to improve the precision of the
$H_0$ measurement with SNe Ia in the NIR in the future, we would need to
increase the number of calibrator SNe Ia, be able to extend the
Hubble-Lema\^itre diagram to higher-z, and include standardization procedures
to help reducing the NIR intrinsic scatter.
