A novel mechanism of photo-orientation of azobenzene-containing liquid-crystalline materials is proposed. This mechanism is based on the notion of photochemically induced domain rearrangement driven by destabilization of liquid-crystalline phase in light absorbing domains due to photochemical formation of non-mesogenic cis-azobenzene moieties. The experimental evidence of photoinduced movement of a domain boundary is presented, and the velocity of this movement is measured. A mathematical model for photo-orientation of a polydomain azobenzene-containing material is formulated. The values of model parameters for a liquid-crystalline azopolymer have been measured in separate experiments. Theoretical predictions demonstrate quantitative agreement with the experimental observations.