The girls are assumed to be seven or eight years old.
Police in the town of Maiduguri, Borno state said that the attack happened when the market was crowded with shoppers, reports BBC.
Witnesses said the girls detonated their explosives minutes apart and both were killed.
No group has said it was behind the bombings but Boko Haram militants have carried out similar attacks.
In the past few months, the Nigerian army has made gains against the group but it still carries out regular bombings.
A member of a militia in Maiduguri, Abdulkarim Jabo, told media the girls were aged about seven or eight and had arrived at the market in a rickshaw.
"They got out of a rickshaw and walked right in front of me without showing the slightest sign of emotion," he said.
"I tried to speak with one of them, in Hausa and in English, but [they] didn't answer. I thought they were looking for their mother."
He said the first girl had headed towards a market stall and then detonated her belt of explosives.
Militants have carried out a string of deadly attacks in north-east Nigeria in recent weeks.
On Friday, a double suicide attack carried out by female bombers killed at least 45 people and wounded 33 at a marketplace in the town of Madagali.
In October, female suicide bombers also killed 17 people at a camp for displaced people in Maiduguri.