The injured children were receiving medical attention following the incident, which took place on Wednesday in Nigeria's third-largest city, Oyo State Police Command said.
"Eight persons have since been arrested for their various involvements", police spokesperson Adewale Osifeso said in a statement.
Among those detained was the main sponsor of the event at the Basorun Islamic High School, which was organised by the Wings Foundation and Agidigbo FM radio.
The Homicide Section of the State Criminal Investigation Department has opened a probe, Osifeso added.
Nigerian President Bola Tinubu on Thursday in a statement "expressed profound sadness over the tragic incident".
He offered his "heartfelt condolences" to locals, state authorities and the "grieving families who have lost their beloved children".
He urged the "Oyo State government to take every necessary measure to prevent such a tragedy from reoccurring", the statement by the presidency added.
