We present an automatic classification strategy for early and accurate assessment of burn injuries using terahertz (THz) time-domain spectroscopic imaging. Burn injuries of different severity grades, representing superficial partial-thickness (SPT), deep partial-thickness (DPT), and full-thickness (FT) wounds, were created by a standardized porcine scald model. THz spectroscopic imaging was performed using our new fiber-coupled Portable HAndheld Spectral Reflection (PHASR) scanner, incorporating a telecentric beam steering configuration and an f-\theta scanning lens. ASynchronous Optical Sampling (ASOPS) in a dual-fiber-laser THz spectrometer with 100 MHz repetition rate enabled high-speed spectroscopic measurements. Given twenty-four different samples composed of ten scald and ten contact burns and four healthy samples, supervised machine learning algorithms using THz-TDS spectra achieved areas under the receiver operating characteristic (ROC) curves of 0.88, 0.93, and 0.93 when differentiating between SPT, DPT, and FT burns, respectively, as determined by independent histological assessments. These results show the potential utility of our new broadband THz PHASR scanner for early and accurate triage of burn injuries.