It happened at The Clutha in Stockwell Street at 22:25 on Friday.
Police Scotland say there were three people on board the helicopter - two officers and a civilian pilot.
Police have not confirmed whether anyone has died but 32 people have been taken to local hospitals. It is not known how many people are still trapped inside the pub.
A senior fire officer said they had made contact with some people trapped inside the pub but the building was unsafe and they were taking a "methodical" approach to the rescue.
It has been reported that about 120 people were in the pub at the time of the crash. Many were rescued or escaped but others have been trapped by a collapse on the left-hand side of the building.

Emergency services have erected barriers around the scene and specialist rescue teams are in the pub with sniffer dogs.
  • Scotland's First Minister Alex Salmond said people must prepare for fatalities
  • The Police Scotland Casualty Bureau number is 0800 092 0410
  • Callers should only contact the Casualty Bureau number if they have concerns for relatives who may have been in the Clutha Vaults pub or surrounding area at the time of the incident
  • The injured have been taken to Glasgow Royal Infirmary, Western Infirmary and the Victoria Infirmary
  • The fire service said there were people trapped in the building but they could not say how many
Some of the injured were taken to a nearby Holiday Inn Express, while more serious casualties were being treated in hospital.
As he left the accident and emergency department of Glasgow Royal Infirmary, a staff member who did not want to be interviewed was asked how serious the injuries were. He replied: "Very".
Glasgow's Health Board said it had put in place its "well-rehearsed major emergency arrangements" and that local hospitals had been on "immediate standby".
A large area of the city centre has been cordoned off.
The emergency services could be seen on the pub's roof trying to rescue people from inside.
The Scottish Fire and Rescue Service said it had a specialist urban search and rescue crew at the scene.
Assistant chief officer Lewis Ramsay said: "Our officers are working very hard in what is a very complex and hard environment for them.
"We are in the process at the moment of making the building stable. It is very unsafe".
He said it was "difficult to tell" how many people were still inside.
He added: "We have had some contact (with those inside) and we are working away just now to make sure that the building is safe in order to get people out.
"We have got 125 firefighters here and they are not only working outside the perimeter of the building, they are working inside. They have been in the cellar, they have been on the roof."
He said "numerous" casualties were removed at the start of the incident and had been taken to hospital and other locations.
Images of the crash showed the wreckage of a dark blue helicopter with a yellow "Police" insignia lying on the pub's roof.
Police Scotland Deputy Chief Constable Rose Fitzpatrick said: "At 22:25 on Friday evening, the Police Scotland helicopter - a Eurocopter EC135 T2 - came down on the roof of the Clutha Vaults pub in Stockwell Street, Glasgow.
"There were three people on board - two police officers and a civilian pilot. There were a number of customers inside the bar at the time."

She said the rescue operation was ongoing and it was too early to provide any details around why the helicopter came down.
Helicopter operator Bond Air Services said it was working with the police and emergency services.
Jim Murphy, the Labour MP for East Renfrewshire, was in the area at the time of the crash and said he ran into the pub to help before emergency services arrived.
He told the BBC there was "pandemonium" as people tried to get out of the pub.
"It was almost like slow motion," he said, adding: "People just formed a bit of human chain, side by side with each other, to help pull injured people out."
The shadow cabinet minister, who had blood on his shirt which he said was not his, described what he saw as a "horrific scene".