We study the structure of atomic hydrogen (H i) in the host galaxy of GRB 171205A/SN 2017iuk at z = 0.037 through H i 21 cm emission line observations with the Karl G. Jansky Very Large Array. These observations reveal unusual morphology and kinematics of the H i in this otherwise apparently normal galaxy. High column density, cold H i is absent from an extended North–South region passing by the optical center of the galaxy, but instead is extended toward the South, on both sides of the galaxy. Moreover, the H i kinematics do not show a continuous change along the major axis of the galaxy as expected in a classical rotating disk. We explore several scenarios to explain the H i structure and kinematics in the galaxy: feedback from a central starburst and/or an active galactic nucleus, ram-pressure stripping, accretion, and tidal interaction from a companion galaxy. All of these options are ruled out. The most viable remaining explanation is the penetrating passage of a satellite through the disk only a few Myr ago, redistributing the H i in the GRB host without yet affecting its stellar distribution. It can also lead to the rapid formation of peculiar stars due to a violent induced shock. The location of GRB 171205A in the vicinity of the distorted area suggests that its progenitor star(s) originated in extreme conditions that share the same origin as the peculiarities in H i. This could explain the atypical location of GRB 171205A in its host galaxy.