Auditory short-term memory (STM) is a key process in auditory cognition, with evidence for partly distinct networks subtending musical and verbal STM. The delayed matching-to-sample task (DMST) paradigm has been found suitable for comparing musical and verbal STM and for manipulating memory load. In this study, musical and verbal DMSTs were investigated with measures of activity in frontal areas with functional near-infrared spectroscopy (fNIRS): Experiment 1 compared musical and verbal DMSTs with a low-level perception task (that does not entail encoding, retention, or retrieval of information), to identify frontal regions involved in memory processes. Experiment 2 manipulated memory load for musical and verbal materials to uncover frontal brain regions showing parametric changes in activity with load and their potential differences between musical and verbal materials. A FIR model was used to deconvolute fNIRS signals across successive trials without making assumptions with respect to the shape of the hemodynamic response in a DMST. Results revealed the involvement of the dorsolateral prefrontal cortex (dlPFC) and inferior frontal gyri (IFG), but not of the superior frontal gyri (SFG) in both experiments, in keeping with previously reported neuroimaging data (including fMRI). Experiment 2 demonstrated a parametric variation of activity with memory load in bilateral IFGs during the maintenance period, with opposite directions for musical and verbal materials. Activity in the IFGs increased with memory load for verbal sound sequences, in keeping with previous results with n-back tasks. The decreased activity with memory load observed with musical sequences is discussed in relation to previous research on auditory STM rehearsal strategies. This study highlights fNIRS as a promising tool for investigating musical and verbal STM not only for typical populations, but also for populations with developmental language disorders associated with functional alterations in auditory STM.