We present an analysis of low resolution infrared spectra for 20 brown dwarf candidates in the core of the $rho$ Ophiuchi molecular cloud. Fifteen of the sources display absorption-line spectra characteristic of late-type stars. By comparing the depths of water vapor absorption bands in our candidate objects with a grid of M dwarf standards, we derive spectral types which are independent of reddening. Optical spectroscopy of one brown dwarf candidate confirms the spectral type derived from the water bands. Combining their spectral types with published near-infrared photometry, effective temperatures and bolometric stellar luminosities are derived enabling us to place our sample on the Hertzsprung-Russell diagram. We compare the positions of the brown dwarf candidates in this diagram with two sets of theoretical models in order to estimate their masses and ages. Considering uncertainties in placing the candidates in the H-R diagram, six objects consistently lie in the brown dwarf regime and another five objects lie in the transition region between stellar and substellar objects. The ages inferred for the sample are consistent with those derived for higher mass association members. Three of the newly identified brown dwarfs display infrared excesses at $lambda$=2.2 $mu$m suggesting that young brown dwarfs can have active accretion disks. Comparing our mass estimates of the brown dwarf candidates with those derived from photometric data alone suggests that spectroscopy is an essential component of investigations of the mass functions of young clusters.
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