Activity in hippocampal area CA1 is essential for consolidating episodic memories, but it is unclear how CA1 activity patterns drive memory formation. We find that in the hours following single-trial contextual fear conditioning (CFC), fast-spiking interneurons (which typically express parvalbumin (PV)) show greater firing coherence with CA1 network oscillations. Post-CFC inhibition of PV+ interneurons blocks fear memory consolidation. This effect is associated with loss of two network changes associated with normal consolidation: (1) augmented sleep-associated delta (0.5-4 Hz), theta (4-12 Hz) and ripple (150-250 Hz) oscillations; and (2) stabilization of CA1 neurons' functional connectivity patterns. Rhythmic activation of PV+ interneurons increases CA1 network coherence and leads to a sustained increase in the strength and stability of functional connections between neurons. Our results suggest that immediately following learning, PV+ interneurons drive CA1 oscillations and reactivation of CA1 ensembles, which directly promotes network plasticity and long-term memory formation.