We present a measurement of the Hubble constant (H-0) using type Ia supernovae (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 SH0ES project. We collected public near-infrared photometry of up to 19 calibrator SNe Ia and 57 SNe Ia in the Hubble flow (z > 0.01), and directly measured their peak magnitudes in the J- and H-band by Gaussian processes and spline interpolation. Calibrator peak magnitudes together with Cepheid-based distances were used to estimate the average absolute magnitude in each band, while Hubble-flow SNe were used to constrain the zero-point intercept of the magnitude-redshift relation. Our baseline result of H-0 is 72.3 +/- 1.4 (stat) +/- 1.4 (syst) km s(-1) Mpc(-1) in the J-band and 72.3 +/- 1.3 (stat) +/- 1.4 (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 SH0ES Cepheid anchors, a photometric zero-point systematic, and a cosmic variance systematic. Our final measurement represents a measurement with a precision of 2.8% in both bands. Among all the analysis variants, the largest change in H-0 comes from limiting the sample to those SNe from the CSP and CfA programs; they are noteworthy because they are the best calibrated, yielding H-0 similar to 75 km s(-1) Mpc(-1) in both bands. We explore applying stretch and reddening corrections to standardize SN Ia NIR peak magnitudes, and we demonstrate that they are still useful to reduce the absolute magnitude scatter and, which improves its standardization, at least up to the H-band. 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, to be able to extend the Hubble-Lemaitre diagram to higher redshift, and to include standardization procedures to help reduce the NIR intrinsic scatter.