Anti-Terrorism Police Unit (ATPU) officers in Kenya are interrogating a British national arrested at Moi international Airport with two magazines and 42 bullets.
Reports indicate Surone Abdiwahid, 27, was arrested at the departure section during the screening of her luggage.
Coast regional police boss Larry Keing said the woman of Somali origin was handed over to the ATPU for further interrogation and profiling.
Police said the woman holds a British passport and was to travel to Nairobi before catching a Kenya Airways flight to London.
"The 9mm ammunition were concealed in her suitcase when they were discovered. We are yet to establish if she is a licensed gun holder and what her intention of smuggling bullets to the plane was," a senior ATPU officer said on Thursday.
The officer, who did not want to be named, said the woman will be taken to court so police seek more days to complete investigations.
He said the government has already contacted the British Embassy in Nairobi to assist in the probe.
"We are working with different agencies and foreigners in the investigation. The incident is being treated as a potential act of terrorism."
The UK government has suffered terrorism attacks carried out by home grown terrorist groups motivated by extremist Islamic ideals.
Islamic State (IS) claimed responsibility for the Manchester suicide bombing and the London Bridge and Borough Market attacks.
Kenyan security agents are also on higher alert following sporadic attacks by terror group al Shabaab in counties including Lamu, Mandera, Garissa and Wajir.
The group has targeted both civilians and security agents.