The footage taken inside the airliner shows a man being violently pulled out of his seat and dragged down the aisle as passengers prepared to take off from Chicago to Louisville on Sunday evening.
The airline in question - United - has tweeted an apology for what happened and says it is investigating.
One 50-second clip of the incident on Twitter was re-tweeted 16,000 times since it was posted that day.
Jayse D Anspach, who posted the footage, tweeted: "#United overbooked and wanted four of us to volunteer to give up our seats for personnel that needed to be at work the next day."
"No one volunteered, so United decided to choose for us. They chose an Asian doctor and his wife."
"The doctor needed to work at the hospital the next day, so he refused to volunteer," Mr Anspach added.
"Ten minutes later, the doctor runs back into the plane with a bloody face, clings to a post in the back, chanting, "I need to go home."
United Airlines incident: What went wrong?
One of the three security officers involved has been "placed on leave", the Chicago Department of Aviation said, and his actions were "obviously not condoned by the Department".
The department also said it would carry out a review into the incident, which it said was "not in accordance with our standard operating procedure".
Another passenger Audra D. Bridges, posted a video of the incident on Facebook that has been viewed over 400,000 times.
She wrote: "Please share this video. We are on this flight. United airlines overbooked the flight."
"They randomly selected people to kick off so their standby crew could have a seat.
"This man is a doctor and has to be at the hospital in the morning," she added.
"He did not want to get off. We are all shaky and so disgusted."
Thousands of Facebook comments have been posted about what happened.
One person wrote: "This is infuriating"
Another posted: "OMG So sad to see someone being treated like this. I wont fly United ever again."
But another felt the video raised some unanswered questions.
"There has to be more to this story," he said.
"Usually when a flight is overbooked they offer free flight vouchers to those willing to change flights or go on standby and a couple of people will jump at those as their travel plans may be flexible."
"I feel like this specific incident HAS to be deeper than what we are seeing in this video," he added.
In a statement United airlines told the BBC: "Flight 3411 from Chicago to Louisville was overbooked."
"After our team looked for volunteers, one customer refused to leave the aircraft voluntarily and law enforcement was asked to come to the gate," the airline added.
The chief executive of United, Oscar Munoz, has since made a statement on Twitter: "This is an upsetting event to all of us here at United. I apologise for having to re-accommodate these customers."
"Our team is moving with a sense of urgency to work with the authorities and conduct our own detailed review of what happened.
"We are also reaching out to this passenger to talk directly to him and further address and resolve the situation," he added.