The Gardai said they “interacted” with the driver of a vehicle, thought to be aged 40, at around 8pm on Sunday in south Dublin.
They were searching for a missing woman who may have been abducted after being forced into a car in Co. Wicklow.
Jastine Valdez, 24, from Enniskerry in the county but originally from the Philippines and studying in Ireland, was last seen when she left her home on Saturday afternoon.
A Garda statement said: “Gardai investigating the disappearance of Jastine Valdez interacted with the driver of a vehicle at approximately 8pm this evening the 20th May 2018 in the Cherrywood area of Dublin.
“An official Garda firearm was discharged.”
A Garda helicopter, cars, support units, and ambulances were at the scene of the shooting at the business park.
Irish broadcaster RTE said the dead man was armed with a knife and was a father-of-two from the Wicklow area.
A Garda statement said she normally regularly contacted her family using social media.
“Contact has stopped so we are very, extremely concerned for her safety. If anybody can help us to locate her we would very much appreciate it.”
Gardai told RTE she was on her way home to Enniskerry when the suspected abduction happened.
“We are looking at that at the moment, trying to clarify her last movements on CCTV and taking statements from witnesses.
“We have a large investigation team working on it.”
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She was reported missing by her family late on Saturday.
Ms Valdez is around 5ft, of slight build with long black hair and brown eyes. When last seen she was wearing a dark coloured jacket, white T-shirt, grey leggings and trainers.