The airplane, operated by Daalo Airlines and flying from Mogadishu to Djibouti with around 60 passengers, landed safely.
Two passengers were slightly injured, police said.
"The passenger plane made an emergency landing soon after it took off yesterday, and there was a damage on one side of the aircraft over the right wing," Somali police officer Mohamed Ise said.
He added it was not clear what had caused the explosion and fire and that investigations were being carried out.
Photographs show a large hole -- about a metre in diameter -- ripped in the side the plane just above the engines on the right wing, with streaks of soot on the plane.