We report the first mid-infrared detection of highly disturbed ionized gas in the ultraluminous infrared galaxy (ULIRG) IRAS F00183-7111. The gas, traced by the 12.81 μm [Ne II] and 15.56 μm [Ne III] lines, spans a velocity range of-3500 to +3000 km s^–1 with respect to systemic velocity. Optical and near-infrared spectroscopic studies show no evidence for similarly high velocity gas components in forbidden lines at shorter wavelengths. We interpret this as the result of strong extinction (A_V = 10-50) on the high-velocity gas, which identifies the base of the outflow traced in 5007 Å [O III] as a plausible origin. Unusual excitation conditions are implied by a comparison of the mid-infrared low-excitation neon line emission and the polycyclic aromatic hydrocarbon (PAH) emission for a sample of 56 ULIRGs. For IRAS F00183-7111, the neon/PAH ratio is 8 times higher than the average ratio. Similar mid-infrared kinematic and excitation characteristics are found for only two other ULIRGs in our sample: IRAS 12127-1412NE and IRAS 13451+1232. Both sources have an elevated neon/PAH ratio and exhibit pronounced blue wings in their 15.56 μm [Ne III] line profiles. IRAS 13451+1232 even shows a strongly blueshifted and broad 14.32 μm [Ne V] line. While for IRAS 13451+1232 the observed [Ne III]/[Ne II] and [Ne V]/[Ne II] line ratios indicate exposure of the blueshifted gas to direct radiation from the AGN, for IRAS F00183-7111 and IRAS 12127-1412NE the neon line ratios are consistent with an origin in fast shocks in a high-density environment, and with an evolutionary scenario in which strongly blueshifted [Ne II] and [Ne III] emission trace the (partial) disruption of the obscuring medium around a buried AGN. The detection of strongly blueshifted [Ne V] emission in IRAS 13451+1232 would then indicate this process to be much further advanced in this ULIRG than in IRAS F00183-7111 and IRAS 12127-1412NE, where this line is undetected.