The principal was arrested on Monday along with the school’s owner and a printing press owner following a complaint by a right-wing Hindu activist, who spotted the map in a school diary.
Police said hundreds of diaries were printed by the private Green Bells Public School in the central state of Madhya Pradesh, showing parts of Kashmir within the borders of Pakistan and China.
Kashmir is divided between India and Pakistan but New Delhi imposes tight restrictions on all printed maps, insisting they show all of Kashmir as being within Indian borders.
The three were denied bail by a court on Tuesday, the officer said, adding they told police that the map had been printed by mistake.
If found guilty, they could be jailed for life under India’s controversial sedition law.
Maps are a highly sensitive issue in India, which has long-running border disputes with several of its neighbours, most famously over the northern state of Jammu and Kashmir.
India recently announced plans for new legislation that provides a $15 million fine and seven-year jail term for those deemed to be publishing incorrect maps.
The government in 2011 ordered The Economist magazine to cover up a map of disputed borders in Kashmir, with white stickers placed over a diagram in thousands of copies on sale in India.
Last year it took television channel Al Jazeera off air for five days after it broadcast what India described as an erroneous map of the region.