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.

Father-of-two Greg Gilbert, 39, from Southampton, has been diagnosed with stage four bowel cancer.
His fiancée Stacey Heale said his only chance of survival was to go abroad for treatment which she said was not available to him on the NHS.
GoFundMe said the appeal was one of the "fastest ever" campaigns on its site.
More than 4,000 people have so far donated to the fundraising page, posted at 10:30 GMT on Wednesday, including music stars Craig David and Ellie Goulding.
In a Facebook post, Mr Gilbert said the response was " truly humbling".
"I can't begin to express our gratitude - not a penny is being taken for granted and we've been moved to tears many times over the last few days reading the supportive messages from not only friends and family but also strangers from all over the world."
Ms Heale said she and Mr Gilbert had been "in tears and holding hands" as they watched the pledges come in.
She said: "It's been overwhelming; our phone has been ringing off the hook. I was refreshing the page this morning and were just like, 'oh my God, we've done it'.
"Grateful doesn't cover it. We've had one person donate £2,000. After such a difficult year for people, to have this at Christmas is so hopeful for us."
Ms Heale said she was researching options for treatment, including personalised immunotherapy in Germany and the USA.
She said she was considering posting a new fundraising target of £250,000, after a private specialist warned that Mr Gilbert's medical bills could amount to £100,000 a year.
Writing on the funding page, Ms Heale said her fiancée had begun chemotherapy for the cancer, which had spread to his lungs.
She said she was disappointed the drug Avastin, for advanced bowel cancers, was currently not routinely available on the NHS.
A fundraising gig has been organised on 5 January at the Southampton venue, the Joiners, where Delays have played many times during their career.
The band was formed in Southampton in 2001 by brothers Greg and Aaron Gilbert with Colin Fox and Rowly.
A number of Japanese manufacturers have suspended operations after two powerful earthquakes hit Kumamoto in south-western Japan.
[NEXT_CONCEPT]
An appeal to pay for cancer treatment for the lead singer of indie band Delays has reached its £100,000 target in 48 hours.