In this work, we consider the flow of a nonionic micellar solution (precursor) through an array of microposts, with focus on its microstructural and rheological evolution. The precursor contains polyoxyethylene(20) sorbitan monooleate (Tween-80) and cosurfactant monolaurin (ML). An irreversible flow-induced structured phase (NI-FISP) emerges after the nonionic precursor flows through the hexagonal micropost arrays, when subjected to strain rates similar to 10(4) s(-1) and strain similar to 10(3). NI-FISP consists of close-looped micellar bundles and multiconnected micellar networks as evidenced by transmission electron microscopy (TEM) and cryo-electron microscopy (cryo-EM). We also conduct small-angle neutron scattering (SANS) measurements in both precursor and NI-FISP to illustrate the structural transition. We propose a potential mechanism for the NI-FISP formation that relies on the micropost arrays and the flow kinematics in the microdevice to induce entropic fluctuations in the micellar solution. Finally, we show that the rheological variation from a viscous precursor solution to a viscoelastic micellar structured phase is associated with the structural evolution from the precursor to NI-FISP.