Test simulated the interception of a long-range missile attack
Iran carried out another attack using ballistic missiles against Kurdish dissidents in 2018 and then against US forces in Iraq in January 2020.
Hoffman said the military had seen symptoms like headaches, dizziness, sensitivity to light and nausea.
The number of service members requiring treatment could increase in coming days.
In his first Friday prayers sermon in eight years, Ayatollah Ali Khamenei also told thousands of Iranians who chanted "Death to America!" that European powers could not be trusted.
When the missiles finally landed at about 1:30 a.m., they struck “empty bunkers that had been evacuated hours before,” the intelligence source said. No one was injured or killed.
The last tweet sent by a user named Sorush before taking off from Iran on a doomed Ukrainian airliner on his way back to university in Canada suggested he knew he was flying into danger.
The crash of the plane caused the deaths of 82 Iranians, 63 Canadians, 11 Ukrainians, 10 Swedes, 4 Afghans, 3 Germans and 3 Britons.
The head of Iran's Civil Aviation authority has said that it could take months to extract information from the voice and flight data recorders.