Police say they have arrested eight people behind the event, including the main organizer, Naomi Silekunola, a well-known figure in the city.
President Bola Tinubu expressed his heartfelt condolences to the parents who lost their children and ordered a thorough investigation.
The Oyo State Government said the victims have been taken to hospitals across Ibadan for treatment after the collision at the Islamic Secondary School in Basharun area of the city.
Authorities urged parents worried about their children’s whereabouts to check with city hospitals.
Doctors at one of the hospitals told the BBC that six children were hospitalized, but only two survived, four died.
At another hospital, a doctor who declined to give his name said he counted three dead bodies.
Some of the affected parents told reporters that they gathered with their children at the venue of the “Christmas Fair at the end of the year” as early as 05:00 on Wednesday — five hours before the start of the event.
They hoped to get money and food, as organizers promised to give 5,000 naira (about £2.50; $3) to 5,000 children, as well as free food for participants.
Nigeria is battling its worst economic crisis in a generation, which explains why more than 10,000 people reportedly turned up for the event.
This year there were several similar incidents.
In March, two female students were crushed to death at Nasarawa State University, Keffi, near the capital Abuja, when a rice distribution program by the state governor sparked a mob. At least 23 people were injured.
Three days later, at least seven people were killed in another stampede in the northern state of Bauchi when a philanthropist and businessman was handing out 5,000 naira handouts.
Earlier in February, five people were reported dead in Lagos when the Nigerian Customs Service auctioned confiscated bags of rice.
A stampede over sacks of rice, which are being auctioned off for about $7:00, left five people trampled to death and dozens more injured.
