We present the first X-ray polarimetric study of the dipping accreting neutron star 4U 1624−49 with the Imaging X-ray Polarimetry Explorer. We report a detection of polarization in the nondip time intervals with a confidence level of 99.99%. We find an average polarization degree (PD) of 3.1% ± 0.7% and a polarization angle of 81° ± 6° east of north in the 2–8 keV band. We report an upper limit on the PD of 22% during the X-ray dips with 95% confidence. The PD increases with energy, reaching from 3.0% ± 0.9% in the 4–6 keV band to 6% ± 2% in the 6–8 keV band. This indicates the polarization likely arises from Comptonization. The high PD observed is unlikely to be produced by Comptonization in the boundary layer or spreading layer alone. It can be produced by the addition of an extended geometrically thin slab corona covering part of the accretion disk, as assumed in previous models of dippers, and/or a reflection component from the accretion disk.