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.
They had already made several other arrests in connection with the video which was shot on 30 January – the day Gandhi was killed.
“We arrested nine people within a week and are searching for two more suspects in the case,” police officer Neeraj Jadaun told the BBC.
Godse, who shot Gandhi in the chest three times at point-blank range on 30 January 1948, was an activist with nationalist right-wing groups, including the Hindu Mahasabha.
Hindu hardliners in India accuse Gandhi of having betrayed Hindus by being too pro-Muslim, and even for the division of India and the bloodshed that marked Partition, which saw India and Pakistan created after independence from Britain in 1947.
This is not the first time the controversial fringe group has tried to glorify Godse and celebrate Gandhi’s assassination.
In 2015, the group announced plans to install statues of Godse across six districts in the southern state of Karnataka, sparking protests across the state.