The crush happened in Chenyi Square in Shanghai's historic Bund district overlooking the Huangpu river.
Thousands of people had gathered to see in 2015.
Social media reports suggest the stampede was triggered by people stopping to pick up fake money thrown from the balcony of a nightclub.
The Shanghai City government said the situation began to deteriorate at 23:35 local time (15:35 GMT) and that a "working group" had been set up to handle the incident.
Photos posted on social media showed people receiving first aid on the road and large numbers of police securing the area.
Many of the dead are believed to be students, with 25 of them women, state media report.
President Xi Jinping has told the Shanghai government to find the causes of the crush as soon as possible, according to state TV.
A traditional new year fireworks display on the Bund had already been cancelled due to official fears of overcrowding, the Shanghai Daily reports.
The BBC's John Sudworth in Shanghai says the investigation may focus on why so many people turned out despite the cancellation and whether there were enough police resources in place to look after them.
'Too many people'
English tourist Rebecca Thomas from Manchester told the BBC she had seen dead bodies on the ground.
"CPR was being given to 10-15 people in the street by loved ones whilst police stood by and watched.
"I asked a police officer if I could help and was told to move along. I saw a man giving his wife or girlfriend mouth-to-mouth on the floor whilst police watched," she said.
"There were really too many people!" wrote one user of Sina Weibo - a Chinese equivalent of Twitter. "Squeezed inside, you could not budge, and could only move with the crowd."
The user, called iiisay, added that traffic police had linked hands to form a human wall after the crush, but the wall was still breached several times.
US photographer Gaby Gabriel told the BBC: "Nobody seemed to be in control and people were crying. It was one of those times when you see the worst in people."
Another Sino Weibo user, Small Metal Makes Steel, said: "At the time there were lots of people, police at the scene maintained order and wouldn't let people near [the scene of the injuries]."
"Lots of people spontaneously linked hands to block the crowds, so the injured had space to settle down, and to allow a clear passage for ambulances," he added.
In a statement, the Shanghai City government said that those hurt had been transferred to hospitals across the city, and that the Shanghai party secretary had visited some of the injured.
Earlier, Shanghai's police department wrote on its verified social media account that some "tourists" had "fallen over" at the Bund, and urged people to leave the area in an orderly fashion.
According to the Shanghai Daily, close to 300,000 people turned up for New Year's Eve celebrations last year, leading to traffic problems.