We present the Parallel, Forward–Backward with Pruning (PFBP) algorithm for feature selection (FS) for Big Data of high dimensionality. PFBP partitions the data matrix both in terms of rows as well as columns. By employing the concepts of p-values of conditional independence tests and meta-analysis techniques, PFBP relies only on computations local to a partition while minimizing communication costs, thus massively parallelizing computations. Similar techniques for combining local computations are also employed to create the final predictive model. PFBP employs asymptotically sound heuristics to make early, approximate decisions, such as Early Dropping of features from consideration in subsequent iterations, Early Stopping of consideration of features within the same iteration, or Early Return of the winner in each iteration. PFBP provides asymptotic guarantees of optimality for data distributions faithfully representable by a causal network (Bayesian network or maximal ancestral graph). Empirical analysis confirms a super-linear speedup of the algorithm with increasing sample size, linear scalability with respect to the number of features and processing cores. An extensive comparative evaluation also demonstrates the effectiveness of PFBP against other algorithms in its class. The heuristics presented are general and could potentially be employed to other greedy-type of FS algorithms. An application on simulated Single Nucleotide Polymorphism (SNP) data with 500K samples is provided as a use case.