The rejection of forward jets originating from additional proton-proton interactions (pile-up) is crucial for a variety of physics analyses at the LHC, including Standard Model measurements and searches for physics beyond the Standard Model. The identification of such jets is challenging due to the lack of track and vertex information in the pseudorapidity range |η|>2.5 . This paper presents a novel strategy for forward pile-up jet tagging that exploits jet shapes and topological jet correlations in pile-up interactions. Measurements of the per-jet tagging efficiency are presented using a data set of 3.2 fb -1 of proton-proton collisions at a centre-of-mass energy of 13 TeV collected with the ATLAS detector. The fraction of pile-up jets rejected in the range 2.5<|η|<4.5 is estimated in simulated events with an average of 22 interactions per bunch-crossing. It increases with jet transverse momentum and, for jets with transverse momentum between 20 and 50 GeV, it ranges between 49% and 67% with an efficiency of 85% for selecting hard-scatter jets. A case study is performed in Higgs boson production via the vector-boson fusion process, showing that these techniques mitigate the background growth due to additional proton-proton interactions, thus enhancing the reach for such signatures.