According to the airline's spokesman Ghassen Ouji, as reported by local media, the incident will be under investigation.
The statement confirmed "an investigation has been opened and that the passengers, at the origin of the incident, could be the subject of prosecution".
"This fight caused a delay of five hours and financial losses were suffered by the company," Mr Ouji added about the flight, reportedly from Tunis to Istanbul.
Thousands of social media users were quick to comment on the video, saying the content was "sad" "sick" and "outrageous".
"This makes me sick and sad. People are desperate entitled and messed up," one person wrote of the altercation.
"Flight attendants don't get paid enough to deal with this," another added.
"This is horrible … I am in shock."
Last month, two women got into a brawl on an American Airlines flight about who would deplane first, wild video shows.
Passenger Annie Victoria Reso captured the fight that broke out when flight 2275 from Los Angeles landed at Phoenix Sky Harbor International Airport on Sunday night local time, the Arizona Republic reported.
The plane landed about 6.30pm but the on-board fighting delayed the other passengers, Ms Reso said.
"Fight broke out as the plane was exiting. Didn't make it off the plane until about 7pm because of the altercation," she wrote on Instagram, where she posted footage of the combatants, adding that she caught her connecting flight at the last second.
Another passenger also shot footage of the fracas – as a flight attendant was heard yelling, "Call for law enforcement! Call for law enforcement!"
Airline spokesman Derek Walls told the New York Post in an email that the company "received a report of an alleged altercation between two customers while waiting to deplane from flight 2275 from Los Angeles (LAX) to Phoenix (PHX)".
He provided no additional details about the incident.
No injuries were reported among passengers or crew members.