Sergei Kozhemyaka, with the southern branch of the Emergency Situations Ministry, said the schools would remain closed until further notice.
Medical workers from Moscow have been taking blood samples trying to establish the cause of the illness. Among the leading theories is poisoning from a type of nerve gas.
Dozens of school-age children from four towns in Chechnya's northeastern Shelkovsky region have been hospitalised, most within the past few days, the Gazeta.ru website reported.
The afflicted, who have also included teachers and school workers, have reported breathing trouble and headaches.
Deputy Chechen Health Minister Zaur Muslyuev said 53 of those sickened were children.
Umar Akhyadov, chief doctor of the Chechen Health Ministry's emergency medicine centre, was quoted by Interfax as saying that the number could rise.
Separatists who have been fighting Russian forces in Chechnya for most of the past decade have committed a series of attacks in Chechnya and other parts of Russia, including the deadly seizure of hostages in a school in the town of Beslan in 2004.
Chechen Prosecutor General Valery Kuznetsov was quoted by the ITAR-Tass news agency as saying earlier that "to speak about a terrorist act is premature" but "all possibilities are being considered."