The firm said passengers were safely evacuated and the fire extinguished.
Traffic was temporarily disrupted on Thursday morning after the vehicle encountered mechanical issues near Southern Bypass Entrance B, which resulted in a fire.
"Our patrol team, working closely with the Kenya Police Service, were able to safely evacuate the passengers aboard the vehicle and extinguish the fire, while keeping other motorists safe," the company said in a statement.
Moja advised drivers to approach the affected area with caution as its teams work to clear debris from the road.
The firm also advised motorists to contact the MOJA Expressway rescue team at 0111039888 in the event of mechanical issues while driving on the Nairobi Expressway.