We propose a simple meson-exchange model of the photoproduction of rho- and omega-mesons off protons near threshold (E(gamma) less than or similar to 2 GeV). This model provides a good description of the available data and implies a large rho-nuclxeon interaction in the scalar channel (sigma-exchange). We use this phenomenological interaction to estimate the leading contribution to the self-energy of rho-mesons in matter. The implications of our calculation for experimental studies of the rho-meson mass in nuclei are discussed.