The open cluster NGC 6791 is among the oldest, most massive, and metal-rich open clusters in the Galaxy. High-resolution H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) of 11 red giants in NGC 6791 are analyzed for their chemical abundances of iron, oxygen, and sodium. The abundances of these three elements are found to be homogeneous (with abundance dispersions at the level of ~0.05-0.07 dex) in these cluster red giants, which span much of the red-giant branch (T eff ~ 3500-4600 K), and include two red clump giants. From the infrared spectra, this cluster is confirmed to be among the most metal-rich clusters in the Galaxy (lang[Fe/H]rang = 0.34 ± 0.06) and is found to have a roughly solar value of [O/Fe] and slightly enhanced [Na/Fe]. Our non-LTE calculations for the studied Na I lines in the APOGEE spectral region (16373.86 Å and 16388.85 Å) indicate only small departures from LTE (<=0.04 dex) for the parameter range and metallicity of the studied stars. The previously reported double population of cluster members with different Na abundances is not found among the studied sample.