Rescuers are focused on Kashima's Aeon shopping center, one of the hardest-hit buildings where the second floor partially collapsed.
The mall also experienced an explosion likely caused by a gas leak, the Aeon president said, though investigations continue.
A cat cafe inside the mall confirmed all 25 cats left during the chaos have been safely rescued.
The Aeon mall had just reopened last month after renovations following damage from a series of strong earthquakes in April 2016 that killed 278 people in the region.
Rescue operations are also underway at a Nippon Paper factory in Yatsushiro city, where at least five people died after a partial collapse.
Eleven people were trapped, seven of whom have been rescued, Nippon Paper said.
The quake, with a shallow depth of 10 km, caused shock across Kumamoto.
One resident said, "I have lived here for 75 years, but I have never experienced such a big quake.
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I thought I would die."
