Several lines of evidence suggest the involvement of prefrontal cortex in time interval estimation. The underlying neural processes are poorly understood, however, in part because of the paucity of physiological studies. The goal of this study was to test the requirement of intact medial prefrontal cortex (mPFC) for performing the task and to find the mechanism of time interval estimation. In Experiment 1, I established a temporal discrimination procedure using six different time intervals ranging from 3018 to 4784 ms that needed to be discriminated as either long or short. Bilateral infusions of muscimol (GABAA receptor agonist) into the mPFC significantly impaired animal’s performance in this task, even when the animals were required to discriminate between only the longest and shortest time intervals. These results show the requirement of intact mPFC in rats for time interval discrimination in the range of a few seconds. In Experiment 2, I then recorded neuronal activity in the mPFC of rats performing the same temporal discrimination task. The recorded neuronal ensemble transmitted a significant amount of information on the elapse of time, suggesting that the mPFC might function as an internal clock. Also, a large fraction of recorded neurons conveyed temporal information by logarithmically changing activity profiles, so that the largest amount of variance in neuronal activity was account for by a logarithmic rather than a linear function, which is more consistent with logarithmic than linear encoding of time. When the range of time interval discrimination varied, activity profiles of mPFC neurons tended to vary according to the range of time interval discrimination, arguing against the possibility that seemingly timing-related neural activity might actually represent sensory response- or motor preparation-related one. These results suggest the rodent mPFC represents the elapse of time based on linearly changing neuronal activity on a logarithmic scale, which might be the reason why the precision of time interval discrimination is lowered in proportion to its duration according to Weber’s law.