Police in the town of Maiduguri, Borno state, said the attack happened when the market was crowded with shoppers.
The girls detonated their explosives minutes apart, witnesses said.
Abdulkarim Jabo, a militia member in Maiduguri, said: "They got out of a rickshaw and walked right in front of me without showing the slightest sign of emotion".
He said the first girl had headed towards a market stall and then detonated her belt of explosives.
The second explosion came slightly later as onlookers rushed to help the victims of the first blast.
No group has taken responsibility for the bombings but Boko Haram militants have carried out similar attacks.
Boko Haram have been fighting Nigeria's government since 2009 to impose hardline Islamic rule over the country's mainly Muslim north.
During those seven years, at least 20,000 people have been killed, more than 2.5 million have had to flee their homes and thousands of women and girls have been abducted by the group.