The incident took place near Felix Houphouet Boigny Stadium where a crowd had gathered to watch fireworks, emergency officials said.
One of the injured, speaking to Reuters at a hospital, said security forces had arrived to break up the crowd, triggering a panic in which many people fell over and were trampled.
"The provisional death toll is 60 and there are 49 injured," Interior Minister Hamed Bakayoko said in a statement broadcast on national television.
President Alassane Ouattara, visiting injured people at the hospital, called the incident a national tragedy and said an investigation was underway to determine what happened.
A Reuters correspondent said blood stains and abandoned shoes littered the scene outside the stadium on Tuesday morning.
"My two children came here yesterday. I told them not to come but they didn't listen. They came when I was sleeping. What will I do?" said Assetou Toure, a cleaner.
She did not know if her children had escaped unhurt.
The incident was the worst of its kind in Abidjan since 2010, when a stampede at a stadium during a football match killed 18 people.
Ivory Coast, once a stable economic hub for West Africa, is struggling to recover from a 2011 civil war in which more than 3,000 people were killed.