Police named the shooter as Boonlet Thanom-anantakun, 42, who fired 22 shots when the son criticised the stall he ran in front of the pharmacy as dirty.
The shooter turned himself in to police soon after the shooting at 5pm in Phuket's Tunthong district.
The bodies of the man and the woman lay on the ground outside the premises.
The killer was explaining what happened to officers at Tungthong Police Station.
The dead - probably mother and son - were named as Worapatr Tirstantayaporn, 35, and Puangrut Tirstantayaporn, 57.