The robbery took place at the McColls store in Longstock Crescent, at around 6.15am on Monday 11 February.
Cash and cigarettes were taken.
Officers previously 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.
The 21-year-old has been released from custody but remains under investigation and the 17-year-old has been released under police bail.
Detectives then arrested another person in connection with the robbery, a 21-year-old man from Southampton. He was released from custody but remains under investigation.
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.