The youths, including one who became nauseous, were stricken in a classroom at Sacred Heart Church on C Avenue shortly after 9 a.m., according to the fire department.
Church officials evacuated the school, and paramedics tended to at least two children who had fainted and a third who reported feeling sick, Coronado Fire Chief John Traylor told News 8.
A total of 17 youngsters and five adults were taken to a hospital for evaluations.
"None of them are critical," Traylor said.
Air quality readings inside the school indicated unusually high levels of carbon monoxide, the chief said.
The pastor of the church, Father Michael Murphy, told the news station the children took ill during a Mass celebrated to mark the last day of school for the congregation's students. An awards ceremony was to follow the service, he said.
"After about seven or eight minutes into the Mass, two children passed out and a third child was feeling nauseous, so they were taken outside to give them some air," Murphy said. "In the meantime, I asked the children to sit down. We prayed a little bit to calm them down."
The priest said he then re-started the service, but was soon interrupted by emergency personnel who asked for the church to be evacuated.
Crews were still trying to determine the source of the problem in the late morning, according to the fire chief.
"I think the situation is under control at this time," Traylor said shortly after 11 a.m.