We present low-resolution (R∼500) near-infrared spectra of 46 candidate young stellar objects in the Chamaeleon I star-forming region recently detected in several deep photometric surveys of the cloud. Most of these stars have K<12. In addition, we present spectra of 63 previously known southern hemisphere young stars mainly belonging to the Chamaeleon I and Lupus dark clouds. We describe near-infrared spectroscopic characteristics of these stars and use the water vapor indexes to derive spectral types for the new objects. Photometric data from the literature are used to estimate the bolometric luminosities of all sources. We apply the pre-main-sequence evolutionary tracks and isochrones of D'Antona & Mazzitelli to derive masses and ages. We detect two objects with mass below the H-burning limit among the 46 new candidates. One of these objects (PMK99 IR Cha INa1) is the likely driving source of a bipolar outflow in the northern region of the cloud. Combining our targets with previously known members of the cloud we analyze the mass and age distributions for 145 stars in the Chamaeleon I dark could. The mass histogram rises from about 2.5 up to 0.4 M☉and then falls off. The median mass is 0.30 M☉. The current population with masses greater than 0.4 M☉is essentially complete. The scarcity of very low mass members is interpreted as population bias toward the least massive and fainter objects. If we assume the true Chamaeleon I initial mass function is flat (in logarithmic mass bins) in the interval 0.4-0.04 M☉as recently found by Comerón et al. in the central 300 arcmin2 region, then we estimate that ∼100 stars remain to be found in that mass range. The distribution of ages indicates an active star-formation episode within the last ∼5x105 yr and a decreasing rate at older ages (a few times 107 yr).