Gardaí were called to the scene of the robbery in the Grange Road area of Baldoyle at about 4.30pm today.
They spotted a vehicle attempting to flee the area and gave chase, which took them through the Darndale area of Coolock.
The man was taken into custody following the car chase through the north Dublin community.
The man, who is in his 30s, is currently being detained at Raheny Garda Station.
Nobody was injured in either the robbery or the pursuit.