The robbery took place at the McColls store in Longstock Crescent, at around 6.15am on Monday 11 February.
Cash and cigarettes were taken.
Today (Feb 14) officers have arrested a 17-year-old boy from Southampton on suspicion of robbery and a 21-year-old man from Southampton on suspicion of assisting an offender.
They remain in police custody at this time.
On Tuesday 12 February, officers arrested a 15-year-old boy from Southampton on suspicion of robbery. He was charged the next day the robbery, plus six other offences.
Anyone with information should call police on 101, quoting Operation Assessment or 44190050130.