New York Governor Andrew Cuomo said the 54-storey office building close to Times Square shook from the impact.
Governor Cuomo said the crash sparked a rooftop fire, which was brought under control. Some were evacuated from the tower, but none were hurt.
He said New Yorkers have "a level of PTSD from 9/11" when they hear news of an aircraft crash in Manhattan.
The pilot has been named by local media as Tim McCormack.
He was the only person aboard the Agusta A109E helicopter, said the Federal Aviation Administration (FAA).
The incident happened at around 14:00 (18:00GMT) on a rainy and foggy Monday on Seventh Avenue.
Governor Cuomo said preliminary reports indicate there was no indication of foul play.
He told reporters at the scene: "There was a helicopter that made a forced landing, emergency landing, or landed on the roof of the building for one reason or another.
"There was a fire that happened when the helicopter hit the roof. People that were in the building said that they felt the building shake."
He added: "If you're a New Yorker, you have a level of PTSD, right, from 9/11. And I remember that morning all too well.
"So as soon as you hear an aircraft hit a building, I think my mind goes where every New Yorker's mind goes."
No debris was visible on the pavement or road below the scene of the AXA Equitable building, which is about 750ft (229m) high.
Michaela Dudley, of Hoboken, New Jersey, was working in the building that the helicopter crashed into. and described feeling "a small tremor".
"I started hearing the blare of sirens and knew something bad had happened," the 30-year-old lawyer said.
"There was a flood of sirens outside and an announcement for us to leave the building. I grabbed my backpack and cell phone.
"The stairwell was packed with people trying to get out and so it was a really slow process. We didn't know what was happening so people were getting a bit panicky."
According to Mayor Bill de Blasio, there is no helicopter landing pad on the roof of the tower at 787 Seventh Avenue.
New York Commissioner James O'Neill told a news conference the helicopter was engaged in "executive travel" at the time of the crash.
The city's top police officer added that the aircraft had taken off from a helipad on 34th Street and may have been heading to its home airport in Linden, New Jersey.
Mr O'Neill said its reason for flying in such poor weather will be "part of the investigation".
Mr de Blasio said it was "an unusual situation for sure", and the helicopter would have needed special permits from LaGuardia Airport in Queens, New York City, to fly so close to Trump Tower.
He described the helicopter as "obliterated".
"There is no indication at this time that this was an act of terror and there is no ongoing threat to New York City," added the mayor.
The National Transportation Safety Board will investigate the incident.
The White House said President Donald Trump had been briefed on the incident.
Last month a helicopter crashed into the Hudson River, falling just short of a heliport.
Five people were killed in 2018 when a sightseeing helicopter plunged into the East River.