The suprachiasmatic nucleus (SCN) of the hypothalamus consists of a highly heterogeneous neuronal population networked together to allow precise and robust circadian timekeeping in mammals. While the critical importance of SCN neurons in regulating circadian rhythms has been extensively studied, the roles of SCN astrocytes in circadian system function are not well understood. Recent experiments have demonstrated that SCN astrocytes are circadian oscillators with the same functional clock genes as SCN neurons. Astrocytes generate rhythmic outputs that are thought to modulate neuronal activity through pre- and postsynaptic interactions. In this study, we developed an in silico multicellular model of the SCN clock to investigate the impact of astrocytes in modulating neuronal activity and affecting key clock properties such as circadian rhythmicity, period, and synchronization. The model predicted that astrocytes could alter the rhythmic activity of neurons via bidirectional interactions at tripartite synapses. Specifically, astrocyte-regulated extracellular glutamate was predicted to increase neuropeptide signaling from neurons. Consistent with experimental results, we found that astrocytes could increase the circadian period and enhance neural synchronization according to their endogenous circadian period. The impact of astrocytic modulation of circadian rhythm amplitude, period, and synchronization was predicted to be strongest when astrocytes had periods between 0 and 2 h longer than neurons. Increasing the number of neurons coupled to the astrocyte also increased its impact on period modulation and synchrony. These computational results suggest that signals that modulate astrocytic rhythms or signaling (e.g., as a function of season, age, or treatment) could cause disruptions in circadian rhythm or serve as putative therapeutic targets.