The accident happened on Sunday near Ndassima, 440km (273 miles) east of the capital, Bangui, said a presidential spokesman.
He said that three days of national mourning had been declared.
CAR is rich in gold and diamonds but has suffered years of conflict – rebels ousted the president in March.
Presidential spokesman Prosper Ndouba said he feared that more people could die.
“The toll of 37 is provisional as there were many injured,” he said.
An unnamed local official told the AFP news agency that dozens of miners had been working beneath the surface, which had become a muddy swamp when they were trapped.
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