Very young (t<~10Myr) stars possess strong magnetic fields that channel ionized gas from the interiors of their circumstellar disks to the surface of the star. Upon impacting the stellar surface, the shocked gas recombines and emits hydrogen spectral lines. To characterize the density and temperature of the gas within these accretion streams, we measure equivalent widths of Brackett (Br)11-20 emission lines detected in 1101 APOGEE spectra of 326 likely pre-main-sequence accretors. For sources with multiple observations, we measure median epoch-to-epoch line strength variations of 10% in Br11 and 20% in Br20. We also fit the measured line ratios to predictions of radiative transfer models by Kwan & Fischer. We find characteristic best-fit electron densities of n_e_=10^11^-10^12^cm-3, and excitation temperatures that are inversely correlated with electron density (from T~5000K for n_e_~10^12^cm^-3^ to T~12500K at n_e_~10^11^cm^-3^). These physical parameters are in good agreement with predictions from modeling of accretion streams that account for the hydrodynamics and radiative transfer within the accretion stream. We also present a supplementary catalog of line measurements from 9733 spectra of 4255 Brackett emission-line sources in the APOGEE Data Release 17 data set.