Frequency conversion of nonclassical light enables robust encoding of quantum information based upon spectral multiplexing that is particularly well-suited to integrated-optics platforms. Here we present an intrinsically deterministic linear-optics approach to spectral shearing of quantum light pulses and show it preserves the wave-packet coherence and quantum nature of light. The technique is based upon an electro-optic Doppler shift to implement frequency shear of heralded single-photon wave packets by ±200 GHz, which can be scaled to an arbitrary shift. These results demonstrate a reconfigurable method to controlling the spectral-temporal mode structure of quantum light that could achieve unitary operation.