A Bayesian framework is presented for finite element model-updating using experimental modal data. A novel likelihood formulation is proposed regarding the inclusion of the mode shapes, based on a probabilistic treatment of the MAC value between the model predicted and experimental mode shapes. The framework is demonstrated by performing model-updating for the Metsovo bridge using a reduced high-fidelity finite element model. Experimental modal identification methods are used in order to extract the modal characteristics of the bridge from ambient acceleration time histories obtained from field measurements exploiting a network of reference and roving sensors. The Transitional Markov Chain Monte Carlo algorithm is used to perform the model updating by drawing samples from the posterior distribution of the model parameters. The proposed framework yields reasonable uncertainty bounds for the model parameters, insensitive to the redundant information contained in the measured data due to closely spaced sensors. In contrast, conventional Bayesian formulations which use probabilistic models to characterize the components of the discrepancy vector between the measured and model-predicted mode shapes result in unrealistically thin uncertainty bounds for the model parameters for a large number of sensors.