"Sadly, we have had 20 fatalities and 11 other seriously injured," said Amir Cicek, the governor of Mugla province, calling it a "horrible accident."
His deputy Kamil Koten said the bus plunged through a crash barrier and fell 15 metres (50 feet) on to a lower road, smashing a car with its three occupants.
"If we count these three deaths, the number of the dead rises to 23," the state-run Anadolu news agency quoted him as saying.
Cicek told NTV television an investigation was under way.
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"The bus's brakes may have malfunctioned," he said.
Television images showed the yellow bus lying on its side and bodies wrapped up in cloth lined up next to it.
Turkish President Recep Tayyip Erdogan, currently on a visit to China, said he was "extremely pained" by the tragedy and asked local authorities to take measures to ensure that "such tragedies" do not recur.
The Hurriyet newspaper quoted Marmaris mayor Ali Acar as indicating an "error by the driver", without giving further details.
Marmaris is one of the country's main resorts on the Mediterranean, and a popular weekend destination for many Turks as temperatures climb.