The arrests took place in Bursa, Istanbul, the southeastern city of Sanliurfa and Afyon in central Turkey, Anatolia news agency said.
Wednesday's bombing, the latest attack to strike Turkey, took place near Bursa's 14th century Grand Mosque, a historic symbol of the city that was the first capital of the Ottoman empire.
Of the 13 who were hurt, eight were still in hospital on Thursday. None of them suffered critical injuries, local officials said.
Nobody has yet claimed responsibility for the attack, which was carried out by a woman, according to Prime Minister Ahmet Davutoglu.
Local newspapers however said the Islamic State group, which is blamed for previous deadly attacks in Turkey, was likely behind the latest assault.
They also said the bomber may have detonated her explosives prematurely, avoiding a higher toll. Police have taken her fingerprints and experts are carrying out DNA tests to identify her.
Turkey remains on high security alert after a series of deadly attacks since last summer blamed on IS and Kurdish rebels.
The latest attack came a day after the US embassy in Ankara warned tourists in Turkey of possible threats as the summer season approaches.
