The state news agency reported that three blasts occurred near the southern coastal area of Marmaris early on Monday and another in Istanbul late on Sunday.
In Marmaris, the first of three explosions hit holidaymakers in a minibus on one of the town’s main streets, packed with bars and restaurants.
Ten Britons and 11 Turks on the bus were injured. The bomb appeared to have been placed under one of the seats.
About 45 minutes later, two bombs exploded in rubbish bins in the city but there were no injuries.
Six of the Britons were taken to the Ahu Hetman hospital in Marmaris, the other four to the Caria hospital.
A spokesman at the Ahu Hetman hospital in Marmaris said none of the victims suffered life-threatening injuries.
At the Caria hospital a hospital spokeswoman said a 13-year-old girl and a 73-year-old woman had undergone surgery.
The other two Britons at the Caria hospital were a 38-year-old man and a 44-year-old woman.
All four had suffered burns and shrapnel injuries to their legs, the spokeswoman said.
Police explosive experts were inspecting the blast sites in Marmaris.
Temal Kocalar, the local governor, said: “We will catch the perpetrators of these explosions in the shortest time possible and bring them before the public.”
The Istanbul blast was in a poor neighbourhood of the Bagcilar district near the local governor’s office. It injured six people, one critically, police said.
Anatolian news agency quoted the Istanbul police chief, Celalettin Cerrah, as saying six people had been injured when a device exploded near a school in Istanbul’s Bagcilar.
“They left a package on a road against the garden wall … At around 2130 [1830 GMT] it exploded and six citizens were injured,” Cerrah said, but did not provide further details of whether it was a bomb and who planted the device.
The tourist industry is a powerful motor of the Turkish economy, hoped to reach $20billion in revenues and 26 million visitors this year.
Marmaris is popular with west European and Russian tourists as well as Turks – for many the last weekend of their annual summer holiday.
No one has claimed responsibilty for the attacks.
Kurdish separatists, leftists and Islamist militants have carried out bomb attacks in Turkey in the past.
The blasts came only two days after two bombs exploded in the southern Turkish city of Adana, injuring four people.
The outlawed Kurdistan Workers Party (PKK), which launched a separatist campaign in 1984, and other groups have been blamed or claimed responsibility for similar blasts in the past.
Turkey, like the United States and European Union, considers the PKK a terrorist organisation and blames it for the deaths of more than 30,000 people.
Ankara has recently increased its troop presence in the mainly Kurdish southeast, where security forces are battling PKK fighters.