The K2Cr8O16 compound belongs to a series of quasi-1D compounds with intriguing magnetic properties that are stabilized through a high-pressure synthesis technique. In this study, a muon spin rotation, relaxation and resonance (μ+SR) technique is used to investigate the pressure dependent magnetic properties up to 25 kbar. μ+SR allows for measurements in true zero applied field and hereby access the true intrinsic material properties. As a result, a refined temperature/pressure phase diagram is presented revealing a novel low temperature/high pressure (pC1 = 21 kbar) transition from a ferromagnetic insulating to a high-pressure antiferromagnetic insulator. Finally, the current study also indicates the possible presence of a quantum critical point at pC2 ~ 33 kbar where the magnetic order in K2Cr8O16 is expected to be fully suppressed even at T = 0 K.