Abstract Feedback and outflows in galaxies that are associated with a quasar phase are expected to be pivotal in quenching the most massive galaxies. However, observations targeting the molecular outflow phase, which dominates both the mass and momentum and removes the immediate fuel for star formation, are limited in high- z QSO hosts. Massive quiescent galaxies found at z ∼ 4 are predicted to have quenched star formation already by z ∼ 5 and undergone their most intense growth at z > 6. Here, we present two Atacama Large Millimeter/submillimeter Array (ALMA) detections of molecular outflows, traced by blueshifted absorption of the OH 119 μ m doublet, from a sample of three z > 6 infrared luminous QSO hosts: J2310+1855 and P183+05. OH 119 μ m is also detected in emission from P183+05, and tentatively in the third source: P036+03. Using similar assumptions as for high- z dusty star-forming galaxy outflows, we find that our QSOs drive molecular outflows with comparable mass outflow rates, which are comparably energetic except for J2310+1855's significantly lower outflow energy flux. We do not find evidence, nor require additional input from the central active galactic nucleus (AGN) to drive the molecular outflow in J2310+1855, but we cannot rule out an AGN contribution in P183+05 if a significant AGN contribution to L FIR is assumed and/or if the outflow covering fraction is high (≥53%), which evidence from the literature suggests is unlikely in these sources. Differences observed in the blueshifted absorption spectral properties may instead be caused by the QSO hosts’ more compact dust continuums, limiting observations to lower altitude and more central regions of the outflow.