None of the 135 passengers on board was hurt in the incident in the south-western city of Mahshahr.
The Caspian Airlines flight departed from Tehran. Its wheels did not appear to be fully down for the landing.
Images and footage of passengers exiting the aircraft were posted on social media.
State TV quoted provincial aviation officials as saying the pilot “landed the aircraft too late and this caused him to miss the runway”.
A reporter who was on board the aircraft said that the back wheel of the McDonnell Douglas plane had broken off and that the plane skidded without its wheels.
Civil aviation spokesman Reza Jafarzadeh told the semi-official Isna news agency that the plane skidded off the runway at 07:50 local time (04:20 GMT) on Monday. He added that an investigation was under way.
Iran has a poor aviation safety record. Sixty-six people were killed in a plane crash in February 2019, while dozens were killed when an IranAir plane broke into pieces upon landing in 2011.