The hole in the plane’s side appeared shortly after take-off from Mogadishu at 10,000ft (3,048m), a colleague of one of the passengers told the BBC.
It is not clear what caused the damage. Officials say two passengers were hurt.
The Daallo Airlines flight, bound for Djibouti, was carrying about 60 people on board, a police officer at the scene told the Bloomberg news agency.
Some reports say a fire broke out shortly after take-off.
Darren Howe, who had a colleague on the plane, took a photo of the damaged aircraft after it had landed.
“It was not an explosion but a fuselage failure at 10,000ft,” he told the BBC.
Daallo Airlines flies regularly from its base in Dubai to Somalia and Djibouti.