The attack took place at around 5:30 pm (local time) on Adan Square, one of the main access points for the Shiite shrine of Kadhimiyah, which attracts many visitors on Saturdays.
"The first explosion was a suicide car bomb and then there was a bomber with a suicide vest," a police colonel said.
He said initial reports were of 13 killed and 37 wounded. A source at the nearby Kadhimiyah hospital confirmed the casualty toll.
Adan Square has been repeatedly hit by attacks. More than 20 people died in a suicide bombing there in February.