Electronics giant Sony, as well as automakers Honda and Toyota cited damage at their plants.
The quakes killed at least 41 people and have caused severe destruction to buildings and infrastructure.
The suspensions in Kumamoto, a manufacturing hub, could cause supply chain disruptions.
Chipmaker Renesas Electronics also said there had been damage to some equipment at its Kumamoto plant, which produces micro-controller chips for cars.
Toyota said it would suspend operations at most assembly plants across Japan. The suspension across Toyota's facilities will be done in stages, and will last for about a week.
The world's biggest car manufacturer said it had been unable to source parts from some of its suppliers. This includes its affiliate Aisin Seiki which is a key supplier for Toyota.
Japan's Nikkei newspaper has reported that Aisin Seiki has been forced to stop producing doors, engines and other parts at its subsidiary in the Kumamoto prefecture, as the area is still experiencing aftershocks. The company is making plans to shift production to other facilities at home and abroad.
The staggered suspension across Toyota's plants is expected to lead to a drop in production, by about 50,000 vehicles, the Nikkei said citing industry analysts.
Sony said at the weekend it was assessing damage at its factory producing image sensors for smartphones, and that the plant would remain closed.
The earthquake in Kumamoto has also affected restaurants and retailers in the area. Supermarket operator Aeon kept all 27 stores in the area shut on Sunday.
A number of Japanese manufacturers have suspended operations after two powerful earthquakes hit Kumamoto in south-western Japan.