Margaret Hill, the daughter of an expatriate worker, was grabbed from a car on her way to school in the oil city of Port Harcourt.
Her mother, Oluchi, told the BBC that the kidnappers had called her demanding a meeting in a town in the Niger Delta.
She said they then allowed her to speak to her daughter who was crying.
Margaret was snatched by gunmen at 0730 (0630 GMT) on Thursday after they smashed a window of her car as it stood in traffic.
Her father Mike Hill, who has lived in the country for 10 years, runs a bar in Port Harcourt.
Mrs Hill, a Nigerian national, said the kidnappers told her to meet them in a town in Bayelsa State in the Niger Delta region, but that neither she nor the police had been able to locate it.
"They say I can bring my husband to swap with the baby," she said. "He wanted to go down for his baby but the police commander told him not to."
The kidnappers then threatened to kill Margaret if Mr Hill did not come within three hours, she said.
Mrs Hill said she had not been contacted by the kidnappers since then.
The UK's Foreign Office has called for the "immediate safe release" of the girl.
The kidnapping follows that of five oil workers on Wednesday, the first since the main militant group in that area - the Movement for the Emancipation of the Niger Delta (Mend) - called off a month-long ceasefire.
Mend has said it had nothing to do with that attack.
The BBC's Alex Last in Lagos says there are a plethora of armed gangs operating in the Niger Delta and kidnapping for ransom has become big business.
In almost all previous cases it was foreign oil workers who had been taken hostage but in recent months the children of wealthy Nigerians had also become targets, he added.
More than 100 foreigners have been taken hostage in the region this year.
Correspondents say hostages are usually released after ransom payments that the Nigerian government and oil companies involved always deny.
On Tuesday, Mend announced that it would not extend its month-long ceasefire called to give the new government a chance to set up talks on the restive region.
It said it would also resume abductions and attacks on oil installations.
The group says it has been kept on the sidelines of government-led talks about the future of the Niger Delta.
Although the Delta accounts for more than 90% of Nigeria's income, the region remains highly impoverished, a situation the militants say they want to change with their campaign.