The Hindu Mahasabha had organised an event to "celebrate" the 71st anniversary of Gandhi's assassination.
In the video, Pooja Pandey shoots the effigy with an air pistol after garlanding a picture of Nathuram Godse, who shot the independence leader.
Gandhi has long been seen as too moderate by some right-wing Hindus.
Police had been seeking Ms Pandey's arrest since the video, believed to have been released by her group, emerged last week.
Two police teams were deployed to track her and her husband, who also features prominently in the footage.
