A hospital in the Uki district said it was unable to operate after losing electricity in the earthquake.
"It's become like a field hospital," the head of its administrative department told Japanese public broadcaster NHK.
Another hospital in the city suspended new admissions after treating 86 injured people, including three in serious condition, saying it could no longer accept additional emergency cases.
About 260,000 people across Kumamoto prefecture have been told to seek shelter as damaged buildings, buckled roads and a collapsed bridge reveal the scale of the destruction.
Police received hundreds of emergency calls after the earthquake, including reports of collapsed structures and people in need of rescue.
The epicentre was around 20 kilometers (12.5 miles) south of Kumamoto City, the largest city in the central part of Kyushu island and home to about 700,000 people. Over 100 aftershocks followed the initial quake.
The port city of Yatsushiro was among the worst-hit areas. Part of a local bridge fell into the Kumagawa River, while authorities warned residents to remain alert for further powerful tremors and landslides over the coming week.
The earthquake reached the maximum level of 7 on Japan's seismic intensity scale in some areas.
More than 36,000 homes remained without electricity on Wednesday as temperatures climbed to around 34 degrees Celsius, prompting authorities to issue heatstroke warnings.
'The strongest quake I have ever experienced'
Earthquake survivors have been describing the moment the 7.1 magnitude quake struck Japan's southwestern Kumamoto region.
"It was the strongest quake I have ever experienced," 73-year-old businessman Kanzo Matsuomoto told the AFP news agency. "I'm not sure if the region will recover from the damage."
Tokito Kitagawa was riding his motorcycle at the time of the earthquake and said: "Suddenly, there was a huge noise. I couldn't stay on my feet. I had to crouch down."
Kiyoshi Matsunaga, 74, was heading to the supermarket checkout just a few streets away from the collapsed Aeon shopping mall when the shaking began.
"I was frightened," he told the Associated Press, describing items being scattered from the supermarket shelves.
"I thought a bomb had gone off," Takateru Sonoda, 41, who runs a combined hair salon and café near the mall, told local news agency Jiji Press.
"There were people calling on others to evacuate and sirens were ringing out. Nearby roads were gridlocked, it was a state of panic."
Yuki Kiyozumi, deputy chief priest at a nearby temple, had just returned home from a meeting and was about to feed her cat. She recalled how she had to crawl on the floor because the shaking was so violent and said: "I don't even know if or how we can rebuild again."
Read: Japan Earthquake Death Toll Rises to 13
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