Magnetic resonance fingerprinting (MRF) is an emerging quantitative magnetic resonance (MR) imaging technique that simultaneously acquires multiple tissue parameters (e.g., spin density, T1, and T2) in an efficient imaging experiment. A statistical estimation framework has recently been proposed for MRF reconstruction. Here we present a new model-based reconstruction method within this framework to enable improved parameter estimation from highly under-sampled, noisy k-space data. It features a novel mathematical formulation that integrates a low-rank image model with the Bloch equation based MR physical model. The proposed formulation results in a nonconvex optimization problem, for which we develop an efficient iterative algorithm based on variable splitting, the alternating direction method of multipliers, and the variable projection method. Representative results from numerical experiments are shown to illustrate the performance of the proposed method.