Passengers said the pilot on the Spain-bound Jet2 aircraft at Glasgow Airport slammed on the brakes before they were evacuated from the plane using inflatable chutes.
The incident happened on a 737 plane destined for Alicante at about 7.40am.
Strathclyde Police said five people were taken to the Royal Alexandra Hospital in Paisley and a further 15 were treated at the scene.
No one is understood to have been seriously injured.
Passenger Jean Walker said some people had to jump from the aircraft wing to the ground.
She said: "It was terrifying. We were about to take off and the plane started shuddering and there were lights flashing and smoke and the crew started shouting 'Get out, get out'.
"We were sitting at the wing and the girl opened the door and we went out on the wing, but there wasn't a chute there.
"There were about eight or 10 of us on the wing and I was saying people couldn't come out because there was no chute. Two girls jumped off the wing on to the ground. They were OK.
"Other people got hurt coming down the chutes - they were inflated, but the hostesses were just shouting 'Jump, jump' and people were just banging into each other at the bottom, and about four people were taken to hospital."
Her husband Gordon Walker said: "You better believe it was terrifying. The stewardesses were panicking and shouting (at) people to go one way, then the other. It all happened really quick and I've never seen anything like it."
Another passenger on the flight said the pilot applied the brakes hard just before take-off. Graham Divers, from Glasgow, said: "I could smell smoke as we were accelerating hard.
"One or two passengers, including myself, had our reading light on and when I looked up to the lamps and the ceiling, I could actually see smoke swirling around and I thought, oops, there's something not right here.
"We were accelerating very, very hard down the runway at this stage and I was about to scream out to the cabin crew when obviously the pilot realised there was something wrong and he immediately throttled the engines back and put the brakes on. It's the hardest braking I've ever experienced in my life."
Glasgow Airport said flights were suspended until 10am following the incident, but the runway has since reopened.
Six inbound flights were diverted - two to Edinburgh, two to Manchester, one to Prestwick and one to Aberdeen.
Five flights were cancelled - two inbound from London City and Gatwick and two outbound, and one plane going to Dublin.
The airport said 14 flights were delayed.
Managing director of Jet2 Ian Doubtfire travelled to Glasgow from the company's Leeds base to talk to staff and deal with the incident.
He said: "During the very early part of the take-off, smoke was seen in the aircraft and the cabin crew informed the captain and he stopped the take-off.
"I've talked to the crew extensively about what happened and they said that the exit from the aeroplane was textbook.
"Obviously, they do a lot of training for this and they said that it was done in the required time, as you have to evacuate quickly with smoke on board."
Mr Doubtfire said injuries when evacuating an aircraft via chutes are common.
"It is possible to get injured when evacuating quite fast," he said.
"People often stop at the bottom and others may come and slide into them or whatever, but all the chutes operated normally and the evacuation was textbook."
He added that the passengers onboard the flight will still be able to travel to Spain today.
"We have asked the passengers if they wish to travel to Alicante and most of them want to do so, so we are arranging an aircraft to come and collect them this afternoon and leave around 3pm."
Aviation writer Jim Ferguson said it was too early to determine the cause of the smoke. He said: "Was there a little oil perhaps drifting around in the system somewhere that heated up and got into the air conditioning? It does happen.
"Obviously it shouldn't, but it does occasionally. Oil is pretty sophisticated stuff in aeroplanes. I'm guessing it could even be hydraulic fluid or something.
"But the fumes can be toxic, so you don't mess around. Somebody would have said something, the captain pressed the big red button and everybody left. It's not lightly done."
He added: "There is a history of people being injured evacuating an aircraft. If you get a lot of people throwing themselves down a chute, they might land awkwardly or they may run into someone on the way down.
"Until we have much more information on this incident, it is premature to identify a cause."
The evacuation comes after around 60 passengers had to flee a Thomas Cook plane by emergency chutes when the cabin filled with smoke after landing at Glasgow Airport earlier this month.
The flight from Dalaman in Turkey touched down on October 11 as normal and was on the stand when the incident happened.
Lawyers Irwin Mitchell are representing several passengers involved in the Thomas Cook incident.
Partner Jim Morris, who is a former Boeing pilot, said: "For there to be two such similar events to have occurred in Glasgow within a matter of a few days of each other and with both events involving Boeing aircraft is a cause of significant concern.
"The Air Accidents Investigation Branch (AAIB) will be carefully investigating the cause of each incident and an important aspect will be for them to determine if there are any similarities or links between these two incidents."
He added: "The hundreds of passengers affected by these two Glasgow flights, particularly those suffering injury, will want to know exactly what went wrong.
"At the same time, everyone is keen to ensure that any underlying faults are identified and resolved as soon as possible for the safety of future passengers and crew.
"As well as investigations by the AAIB, we will be undertaking our own assessment of what has gone wrong in Glasgow and we are keen to speak to passengers on board both flights and any other witnesses."