There is conflicting evidence over the ability to modulate mind-wandering propensity with anodal transcranial direct current stimulation (tDCS) over the left dorsolateral prefrontal cortex (prefrontal tDCS). Here, 20 participants received 20-min of active and sham prefrontal tDCS while in the MRI scanner, in two separate sessions (counterbalanced). In each session, they completed two runs of a sustained attention to response task (before and during tDCS), which included probes recording subjective responses of mind-wandering. We assessed the effects of tDCS on behavioural responses as well as functional and effective dynamics, via dynamic functional network connectivity (dFNC) and dynamic causal modelling analyses over regions of the default mode, salience and executive control networks. Behavioural results provided substantial evidence in support of no effect of tDCS on task performance nor mind-wandering propensity. Similarly, we found no effect of tDCS on frequency (how often) or dwell time (time spent) of underlying brain states nor effective connectivity. Overall, our results suggest that prefrontal tDCS is unable to modulate mind-wandering propensity or influence underlying brain function. This expands previous behavioural replication failures in suggesting that prefrontal tDCS may not lead to even subtle (i.e., under a behavioural threshold) changes in brain activity during self-generated cognition.