We use midinfrared pulses with stable carrier-envelope phase offset to drive molecular vibrations in the charge transfer salt ET−F2TCNQ, a prototypical one-dimensional Mott insulator. We find that the Mott gap, which is probed resonantly with 10 fs laser pulses, oscillates with the pump field. This observation reveals that molecular excitations can coherently perturb the electronic on-site interactions (Hubbard U) by changing the local orbital wave function. The gap oscillates at twice the frequency of the vibrational mode, indicating that the molecular distortions couple quadratically to the local charge density.