Three of the explosions struck the seaside resort around midnight (2100 GMT) as many late-night revellers were out on the streets, dotted with bars, restaurants and cafes.
Local governor Temel Kocaklar said 21 people, among them ten British nationals, were injured in the blasts which he implied were bomb attacks.
"We will catch the perpetrators of these explosions in the shortest time possible and bring them before the public," he told the Anatolia news agency.
The CNN-Turk news channel reported that the first blast ripped through a mini-bus travelling on one of the main streets and was caused by a bomb placed under one of the seats.
It was followed shortly by two other blasts in garbage bins, it added.
There have been no claims of responsibility for the blasts.
Police forces at scene of blast in Marmaris (Photo: AP)
A spokesman for the British foreign office told AFP in London that the injured Britons were in local hospitals and four were in serious condition.
None of them suffered life-threatening injuries, a spokesman at the Ahu Hetman hospital in Marmaris told Britain's Press Association.
Among the ten were a 38-year-old man, a 44-year-old woman, a 13-year-old girl and a 73-year-old woman, according to the Press Association, citing a spokeswoman at the Caria Hospital, where four of the Britons were taken.
The latter two have undergone surgery, she said.
She added that all four were injured when the bus exploded in the town's main street, outside a McDonald's restaurant
All four had suffered burns and shrapnel injuries to their legs and "lower extremities", the spokeswoman said.
'Bus was basically blown apart'The blasts took place as many late-night revellers were still out on the town, which is popular with both western European and Turkish tourists, according to one witness.
"It was the usual holidaymakers walking about, everybody was out enjoying themselves," Danielle Pearson told Sky News television in a telephone interview from Marmaris.
"The bus was basically blown apart. The bomb just sounded like a gunshot really," she said.
"The roads were really busy, there were ambulances and police cars going everywhere."
Security was immediately beefed up in the town, with additional forces being called in to check vehicles entering and leaving the area, Anatolia said.
Six people were also injured when a package bomb exploded in Turkey's biggest city Istanbul late on Sunday, the city's police chief Cemalettin Cerrah said.
The device in Istanbul was left by a school in the Bagcilar district in the city's European side and went off around 9:30 pm, Cerrah said, the Anatolia news agency reported.
Oultawed Kurdish rebels, extreme leftists and Islamic militants have all carried out bomb attacks in Turkey in the past, including against tourist resorts.
A radical armed Kurdish group, calling itself the Kurdistan Freedom Falcons (TAK), has claimed responsibility for 12 bomb attacks in urban centres across the country this year, in which six people were killed and more than 100 others injured.
The deadliest of them was at the Mediterranean resort of Manavgat, in which three foreign tourists and a Turk perished.