Police and the British High Commission have named the woman as Faye Mooney, 29, and said they were aware of an incident which took place at a holiday resort on Friday but added that they would not speculate on a motive.
Her next of kin have been informed.
The Briton was working in Nigeria as a communications specialist for aid group Mercy Corps and was one of 12 tourists travelling to the northern city of Kaduna from Lagos, police said.
Police said Ms Mooney, who worked in the west African nation for nearly two years, had been attending a party before the incident.
In a statement, Mercy Corps said it was “utterly heartbroken” by the killing.
A Kaduna state police spokesman said: “Some suspected kidnappers armed with dangerous weapons gained entry into a recreational resort called Kajuru Castle in Kajuru local government area shooting sporadically and in the process shot dead two persons, including an expatriate lady, and took away three others.”
Officers have not yet named the other person killed in the incident.
No individuals or groups have said they are behind the killing and police are yet to identify the kidnappers.
Northern Nigeria has been dealing with a Boko Haram and Islamic State insurgency and clashes between farmers and herders, in which hundreds have died.
Kaduna has seen a spate of kidnappings by armed men in recent months.
In a statement, the British High Commission said: “We are engaging with the Nigerian authorities, and we understand an investigation is under way.”