"Among those arrested are people with hostile motives and with the aim of instilling terror in the people and students and to close schools."
The ministry added that "fortunately, from the middle of the last week until today, the number of incidents in schools has decreased significantly, and there have been no reports of sick students".
The statement pointed at possible links to an Albania-based exiled Iranian opposition group that Tehran considers a "terrorist" organisation, the People's Mujahedin of Iran or Mujahedeen-e-Khalq (MEK).
"The investigation of these criminal people, including the discovery of their possible connection with the terrorist organisations such as the MEK and others, is ongoing," reported IRNA.
The poisonings started two months into the protests that gripped Iran following the September 16 death of 22-year-old Mahsa Amini, an ethnic Kurd who had been arrested over an alleged violation of strict dress rules for women.
Iran has blamed those protests, which it commonly labels "riots", on hostile forces abroad linked to its arch foes the United States, Israel and their allies.
More than 5,000 pupils have been affected in approximately 230 schools across 25 out of Iran's 31 provinces, the latest official tally said.
The ministry said arrests were made in the provinces of Tehran, Qom and Gilan in the north, Razavi Khorasan in the northeast, West Azerbaijan, East Azerbaijan and Zanjan in the northwest, Kurdistan and Hamadan in the west, Khuzestan in the southwest and Fars in the south.
Supreme leader Ayatollah Ali Khamenei had last Monday called for the perpetrators of the "unforgivable crime" to be tracked down "without mercy".