Abstract Brown dwarfs exhibit patchy or spatially varying banded cloud structures that are inferred through photometric and spectroscopic variability modeling techniques. However, these methods are insensitive to rotationally invariant structures, such as the bands seen in Jupiter. Here, we present H-band Very Large Telescope/NaCo linear polarization measurements of the nearby Luhman 16 L/T transition binary, which suggest that Luhman 16A exhibits constant longitudinal cloud bands. The instrument was operated in pupil tracking mode, allowing us to unambiguously distinguish between a small astrophysical polarization and the ∼2% instrumental linear polarization. We measure the degree and angle of linear polarization of Luhman 16A and B to be p _A = 0.031% ± 0.004% and ψ _A = −32° ± 4°, and p _B = 0.010% ± 0.004% and , respectively. Using known physical parameters of the system, we demonstrate that an oblate homogeneous atmosphere cannot account for the polarization measured in Luhman 16A, but could be responsible for that of the B component. Through a nonexhaustive search of banded cloud morphologies, we demonstrate a two-banded scenario that can achieve a degree of linear polarization of p = 0.03% and conclude that the measured polarization of the A component must be predominantly due to cloud banding. For Luhman 16B, either oblateness or cloud banding could be the dominant source of the measured polarization. The misaligned polarization angles of the two binary components tentatively suggest spin–orbit misalignment. These measurements provide new evidence for the prevalence of cloud banding in brown dwarfs while at the same time demonstrating a new method—complementary to photometric and spectroscopic variability methods—for characterizing the cloud morphologies of substellar objects without signs of variability.