Eyewitnesses reported marked and unmarked cars seen blocking the vehicle's escape in Haven Road, Canford Cliffs.
Dorset Police confirmed armed officers had arrested four men "as part of an ongoing investigation" but would not give further details.
People at the scene said they heard what sounded like a gunshot and saw "pink smoke" in the street.
A police spokesman said: "At 15:00 GMT today armed officers stopped a vehicle on Haven Road in Poole and arrested four men as part of an ongoing investigation.
"Due to the nature of the investigation, police are unable to give any more information."
Armed police have arrested four men after swooping on a car in Poole.