The attack took place near the city's 14th Century Grand Mosque, a symbol of the city, reports said.
The governor of Bursa said the attacker was a suspected female suicide bomber.
Turkey has been hit by a wave of suicide bombings blamed on both Islamist and Kurdish militants. Earlier reports said one person had been killed in the blast.
However, Reuters news agency later quoted Turkey's health minister as saying 13 people had been wounded, none seriously.
No-one has yet claimed responsibility for the bombing.
On Tuesday the US warned of "credible indications" of terrorist threats at tourist areas in the country.
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A suicide bomber has struck in the western Turkish city of Bursa, injuring 13 people, officials say.