Other sources gave a much higher toll, saying 17 people including children had been killed.
The deaths in Bauchi city come as Nigeria suffers the worst economic crisis in a generation, and just days after two students died in a crush for free bags of rice in Keffi, in the center of the country.
Early in the morning, women and children gathered outside the office of a wealthy businessman in Bauchi city to receive 5,000 naira ($3.40) cash gifts to help pay for food during the Muslim holy month Ramadan.
Witnesses said members of the crowd pushed to get hold of the money, causing a stampede.
"We received a report from Abubakar Tafawa Balewa Teaching Hospital that five women were brought to the hospital in critical condition following a stampede during cash distribution by the proprietor of Shafa Holdings," said Bauchi state police spokesman Mohammed Wakil.
"Four of the women were confirmed dead while the fifth is still in the hospital receiving treatment," said Wakil, adding that police had launched an investigation.
Shafa Holdings staff member Shafiu Umar said 17 people had died in the crush, including 10 children and seven women.
"The crowd was more than expected and the beneficiaries jostled for the cash donation, leading to a deadly stampede," Umar said.
"We evacuated 17 dead victims, 10 underaged and seven women to the hospital along with several others who sustained injuries."
A security agency officer at the scene also put the death toll at 17.
"A huge number of women came from far and near, some with their children," said the officer who asked not to be identified.
Nigeria has been grappling with soaring food prices since the government withdrew a petrol subsidy and floated the naira currency in a bid to shore up the economy.
Inflation has reached a three-decade high of 31.7 percent, making basic items inaccessible for many.
Most Nigerians live on less than $2 a day and many have had to skip meals and give up products such as meat, eggs and milk.
Earlier this month Nigeria's emergency agency said security had been tightened at its warehouses after hundreds of people looted a food store in the capital Abuja.
Forum