The explosion in the bustling Midan neighbourhood of the Syrian capital wounded three police officers, said the Al-Watan daily, which is close to the government.
"A seven-year-old girl entered the police station, carrying a belt that was detonated from afar," the paper posted on its Facebook page.
A police source told Al-Watan that she had appeared lost and asked to use the bathroom when the explosives went off.
Although rebel groups have fired rockets and mortar rounds into the capital, explosions inside the city itself are rare.
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Syrian state news agency SANA said earlier there were preliminary reports about a "terrorist explosion at the Midan police station in Damascus".
The Syrian Observatory for Human Rights confirmed there had been a blast in Midan but said it could not specify the cause.
Observatory head Rami Abdel Rahman told AFP that "one woman" was killed in the blast, but it remained unclear whether she was a suicide bomber or a bystander.
In early 2012, a suicide bomber killed 26 people when he blew himself up in Midan.
More than 310,000 people have died since Syria's conflict broke out in 2011.