Officers were called to reports of an armed robbery at a garage in New Road, Durrington, at around midnight on Tuesday (December 14).
Two members of staff reported being threatened by a man with a firearm and forced to reopen the store, which had recently been locked for the night.
The suspect stole personal items from the victims, as well as cash from the till and a large amount of tobacco and cigarettes, before making off on foot.
One of the victims suffered minor injuries to her hand.
Officers tracked the suspected offender to a property in a nearby housing estate, containing three occupants.
Two local men aged 32 and 39 and a 29-year-old local woman were arrested on suspicion of robbery and remain in police custody.
Detective Inspector Pauline Lane said: “We understand the impact incidents such as these have on the community and residents can expect to see an increased police presence in the area over the next few days.
“We would like to thank the public for their patience and understanding while the investigation is ongoing.
“Anybody who witnessed the incident or has relevant CCTV, doorbell or dash-cam footage is asked to contact us either online or by calling 101, quoting Operation Quagmire.”