The woman went into the police station in the Sultanahmet district and told the police in English she had lost her wallet before setting off her explosives, governor Vasip Sahin said on Turkish television.
One policeman was badly wounded and died of his wounds in hospital, the official Anatolia news agency reported.
A second policeman was lightly wounded. Both were staffing a tourist police post intended to assist tourists with questions and problems.
"She approached the police at around 5:00 pm (1500 GMT), saying in English: 'I have lost my wallet'. That's all I can say. We are trying to identify the attacker," said Sahin.
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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.
Officials said there was so far no indication of the nationality or identity of the female suicide bomber.
Turkish news reports said two more explosive charges had been found on the corpse of the suicide bomber.
In the first government reaction to the attack, Deputy Prime Minister Numan Kurtulmus condemned the strike as a "heinous terror attack".
"The target of this attacks is the new Turkey, our beloved nation. But they won't succeed. They won't be able to destroy our brotherhood and unity," he write on Twitter.
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.