The incident occurred in the early hours of Tuesday as people were heading home from a fireworks display at a stadium in the cityâ€™s Plateau district.
Most of the dead are believed to be children aged between eight and 15.
Details of what caused the stampede are unclear, but the government has pledged to investigate the tragedy.
The death toll is expected to rise.
The crush happened after the fireworks ended in the 65,000-capacity Felix Houphouet Boigny Stadium at about 02:00 local time.
â€œDuring the fireworks everything was proceeding normally,â€ Interior Minister Hamed Bakayoko said. â€œAt the end of it people wanted to go home, back to their home districts.
â€œNear the Hotel Tiama and the Houphouet-Boigny stadium there was a stampede. We were notified of injuries and deaths, and as regards casualties, we learnt that there was a heavy toll. The circumstances surrounding the incident will form the subject of an investigation.â€
Reports vary as to what caused the crush.
According to some reports, thousands of people were trying to leave the festivities at the same time as another large crowd was arriving, the BBC West Africa correspondent reports.
But one of the wounded told Reuters that the arrival of the security forces had triggered a panic which resulted in a stampede.
â€œThe great mass of people caused a very large stampede which caused 60 deaths, more than 200 people were injured,â€ Lt Col Issa Sako, head of the military rescue effort, told reporters.
â€œIn the stampede, some people were trampled and suffocated by the crowd.â€
At least two hospitals in the city have received the wounded, some reportedly with life-threatening injuries.
President Alassane Ouattara has visited some of the wounded in hospital and promised that the costs of their medical treatment will be covered by the government.
The governor of Abidjan, Robert BeugrÃ© Mambe, said he had also visited the wounded and the families of those who had lost loved ones. â€œWe bow our heads respectfully before the memory of all those who died,â€ he said.
The site of the crush was littered with abandoned clothes and blood stains as light dawned.
Relatives went to the scene to get news of missing loved ones.
The distraught mother of a nine-year-old boy told local media: â€œI have just seen all those bodies, but I canâ€™t find my son.â€
The Felix Houphouet Boigny Stadium was named after the founding president of Cote dâ€™Ivoire.
The fireworks event had been organised to celebrate the peace recently re-established after a period of unrest triggered by former President Laurent Gbagboâ€™s refusal to recognise Ouattaraâ€™s victory in 2010 elections.
The night before the tragedy, the stadium hosted a concert by US performer Chris Brown.