The crush broke out in Chenyi Square in Shanghai’s Huangpu district, Xinhua news agency reported.
The Shanghai City government said the situation began at 23:35 local time (15:35 GMT) and that a “working group” had been set up to handle the incident.
The cause of the crush was currently under investigation, it added.
Photos posted on social media showed people receiving first aid on the road and large numbers of police securing the area.
The photos suggested that large numbers of people had gathered near the waterfront area, known as The Bund.
On social media, users who said they were at the scene described huge crowds at the scene of the crush.
“There were really too many people!” Sina Weibo user iiisay wrote. “Squeezed inside, you could not budge, and could only move with the crowd.”
She added that traffic police had linked hands to form a human wall after the crush, but the wall was still breached several times.
Another 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.