They were detained from Islamic International School in Dhaka's Merul Badda area on Friday. Shamsunnahar Nizami, wife of hanged war criminal Motiur Rahman Nizami, is the principal of the school.
Dhaka Metropolitan Magistrate Sazzadur Rahman issued the remand order for the 18 on Saturday afternoon.
Of them, two --Abadul and Shamim-- were granted three-day remand each while 16 others were placed on two days remand.
Police suspect that the detainees were plotting anti-state activities.