The female bomber went to police in the Sultanahmet district on Tuesday, speaking in English and claiming she had lost her wallet before she blew herself up, Al Jazeera`s Bernard Smith said.
The Sultanahmet district, which is the home of world famous attractions including the Blue Mosque and Aga Sophia museum, is visited by thousands of Turkish and foreign tourists every day.
Emergency services rushed to the scene and the city tram line that goes through the district was halted, reported the AFP news agency.
Ahmet Davutoglu, Turkey`s prime minister, told reporters the bomber was carrying two other bombs, which were safely defused.
"Two separate bombs [that were on the suicide bomber and that didn`t go off] were defused. One policeman is wounded. Police forces and intelligence services are investigating whether there is a link to any group," Davutoglu told reporters in a brief statement in the capital Ankara.
"The most comprehensive investigation will be carried out regarding the attack that was carried out in the heart of Istanbul and when the links to an organisation are found, further steps will be taken."
Turkish station Show TV released grainy security footage purportedly showing the female bomber walking along a street.
Officials said there was so far no indication of the nationality or identity of the bomber.
The attack came five days after a member of an outlawed Marxist group attacked police on guard outside the Ottoman-era Dolmabahce palace in Istanbul on the Bosphorus.
The man, named as Firat Ozcelik, hurled two grenades at the police honour guard on duty outside the palace but they failed to explode.
The Revolutionary People`s Liberation Party-Front (DHKP-C) said it was behind the attack outside the Dolmabahce palace, which houses the Istanbul offices of the Turkish prime minister.
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