Officers were called at 6.36am on Sunday to a Sainsbury's store where a 26-year-old man from Southampton was found with two suspected stab wounds to the shoulder. He remains in hospital to be treated for his injuries, which are serious but not life-threatening.
Enquiries have focused on an address in Saturn Close, where police believe the alleged assault took place sometime during the early hours of Sunday morning.
A 28-year-old man from Southampton and a 20-year-old woman from Southampton were arrested at an address in Saturn Close shortly after 7.30am this morning on suspicion of causing grievous bodily harm (GBH) with intent. They remain in custody for questioning.
Police are conducting forensic and CCTV enquiries in the area.
Anyone with information is asked to phone CID at Southampton Central Police Station on 101. Mini-com users can phone 18001 101. Information can be given anonymously by phoning the independent Crimestoppers charity on 0800 555 111.