An extension of the quantum-classical mean-field (MF) approximation is developed by application of quantized Hamilton dynamics (QHD) to the classical subsystem. The resulting quantized MF (QMF) approach supplements the classical position and momentum variables with higher order moments. In the limit of all moments exact quantum dynamics is achieved. Already with second order variables, QMF properly treats zero point energy (ZPE) that increases quantum transition probabilities and restricts energy exchange between quantum and classical subsystems. The efficiency of QMF and the effect of ZPE on the transition probability are illustrated by application to a model Of O-2 interacting with a Pt surface.