It is becoming increasingly accepted that timing tasks, and underlying temporal processes, can be partitioned on the basis of whether they require an explicit or implicit temporal judgement. Most neuroimaging studies of timing associated explicit timing tasks with activation of the supplementary motor area (SMA). However, transcranial magnetic stimulation (TMS) studies perturbing SMA functioning across explicit timing tasks have generally reported null effects, thus failing to causally link SMA to explicit timing. The present study probed the involvement of SMA in both explicit and implicit timing tasks within a single experiment and using High-Definition transcranial Random Noise Stimulation (HD-tRNS), a previously less used technique in studies of the SMA. Participants performed two tasks that comprised the same stimulus presentation but differed in the received task instructions, which might or might not require explicit temporal judgments. Results showed a significant HD-tRNS-induced shift of perceived durations (i.e., overestimation) in the explicit timing task, whereas there was no modulation of implicit timing by HD-tRNS. Overall, these results provide initial non-invasive brain stimulation evidence on the contribution of the SMA to explicit and implicit timing tasks.