The incident took place near Felix Houphouet Boigny Stadium, where a crowd had gathered to watch fireworks, emergency officials said.
One of the injured 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 a hospital, called the incident a national tragedy and said an investigation was under way to determine what happened.
Reporters said blood stains and abandoned shoes littered the scene outside the stadium yesterday 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 is struggling to recover from a 2011 civil war in which 3000 people were killed.