In this paper, we consider discrete-time linear-quadratic-Gaussian (LQG) mean field games over unreliable communication links. These are dynamic games with a large number of agents where the cost function of each agent is coupled with other agents' states via a mean field term. Further, the individual dynamical system for each agent is subject to packet dropping. Under this setup, we first obtain an optimal decentralized control law for each agent that is a function of local information as well as packet drop information. We then construct a mean field system that provides the best approximation to the mean field term under appropriate conditions. We also show that the optimal decentralized controller stabilizes the individual dynamical system in the time-average sense. We prove an ε-Nash equilibrium property of the set of N optimal decentralized controllers, and show that ε can be made arbitrarily small as the number of agents becomes arbitrarily large. We note that the existence of the ε-Nash equilibrium obtained in this paper is primarily dependent on the underlying communication networks.