In this paper, a novel covariance-based channel feedback mechanism is investigated for frequency division duplexing (FDD) massive multi-input multi-output (MIMO) systems. The concept capitalizes on the notion of user statistical separability which was hinted in several prior works in the massive antenna regime but has not fully exploited so far. We propose a hybrid statistical-instantaneous feedback mechanism where the users are separated into two classes of feedback design based on their channel covariance. Under the hybrid framework, each user either operates on a statistical feedback mode or quantized instantaneous channel feedback mode. The key challenge lies in the design of a covariance-aware classification algorithm which can handle the complex mutual interactions among all users. The classification is derived from rate bound principles and a precoding method is also devised under the mixed statistical and instantaneous feedback model. Simulations are performed to validate our analytical results and illustrate the sum rate advantages of the proposed feedback scheme under a global feedback overhead constraint.