Antimicrobial peptides (AMPs) are cationic amphiphiles that comprise a key component of innate immunity. Synthetic analogues of AMPs, such as the family of phenylene ethynylene antimicrobial oligomers (AMOs), recently demonstrated broad-spectrum antimicrobial activity, but the underlying molecular mechanism is unknown. Homologues in this family can be inactive, specifically active against bacteria, or nonspecifically active against bacteria and eukaryotic cells. Using synchrotron small-angle X-ray scattering (SAXS), we show that observed antibacterial activity correlates with an AMO-induced topological transition of small unilamellar vesicles into an inverted hexagonal phase, in which hexagonal arrays of 3.4-nm water channels defined by lipid tubes are formed. Polarized and fluorescence microscopy show that AMO-treated giant unilamellar vesicles remain intact, instead of reconstructing into a bulk 3D phase, but are selectively permeable to encapsulated macromolecules that are smaller than 3.4 nm. Moreover, AMOs with different activity profiles require different minimum threshold concentrations of phosphoethanolamine (PE) lipids to reconstruct the membrane. Using ternary membrane vesicles composed of DOPG:DOPE:DOPC with a charge density fixed at typical bacterial values, we find that the inactive AMO cannot generate the inverted hexagonal phase even when DOPE completely replaces DOPC. The specifically active AMO requires a threshold ratio of DOPE:DOPC = 4:1, and the nonspecifically active AMO requires a drastically lower threshold ratio of DOPE:DOPC = 1.5:1. Since most gram-negative bacterial membranes have more PE lipids than do eukaryotic membranes, our results imply that there is a relationship between negative-curvature lipids such as PE and antimicrobial hydrophobicity that contributes to selective antimicrobial activity.