Postural instability, a concomitant of falls, can persist in people with alcohol use disorder (AUD) even with sustained sobriety. Balance testing using a force plate, which detects micromovements while standing still, can be quantified with spectral analysis and expressed as temporal frequency, an index of truncal (i.e., postural) tremor. Here, we investigated physiological and brain structural factors that may contribute to a mechanistic understanding of postural instability during quiet standing in AUD. This mixed cross-sectional/longitudinal design included 462 observations in 292 participants (age 25-75 years): 120 men and 44 women with DSM-5-determined AUD and 75 control men and 53 control women. All participants completed balance testing on a force plate under two conditions: eyes open and eyes closed, both with feet together. Most participants also underwent two-point discrimination testing on the soles of the feet and structural MRI, typically within the week of balance testing. Linear mixed-effects models revealed greater tremor in all conditions in the AUD than control group with the diagnostic differences attributed to AUD men. Age effects did not differ significantly between AUD and control groups. By contrast, stronger correlations were detected between greater tremor, measured as a 2-5 Hz/0-2 Hz frequency quotient, and smaller regional brain volumes selective to motor centers (frontal supplemental motor cortex, thalamus, pallidum, cerebellar white matter) of the AUD men. The salient signs of postural instability were attributable to AUD men who consumed alcohol exceeding NIAAA guideline limits in the year prior to testing.