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The ferry, MV Barima, departed from the capital, Georgetown, on Saturday afternoon local time, headed for Port Kaituma, in the north of the country.
The 40m-long (131ft) vessel was built in 1939, according to a listing on VesselFinder.
A survivor, Elena Moonsammy, told local news site Kiskadee Watch, external that the ferry had tilted after being hit by a large wave, with water quickly rushing in.
It started to take on water within seconds, she said.
A distress call was received at 23:01 (03:01 GMT Sunday), triggering a search operation involving government teams and privately owned boats.
Moonsammy said she had survived by clinging to a box floating amidst the debris.
She had tried to hold on to the hand of her two-year-old child but they had been separated.
Moonsammy said she had managed to save a woman, whom she urged to also hold on to the floating box.
At least 15 children were among those rescued. Small private boats were key in pulling at least 17 survivors from the sea.
The French army sent 12 divers, two doctors and a mechanic from nearby French Guiana to aid the search-and-rescue operation.
Guyana’s Health Minister, Dr Frank Anthony, said three of the survivors remained in hospital with minor injuries but the others had already been discharged.
Most, he added, had cuts and bruises from clinging to debris for hours.
