Officers were called to the reserve at 8.21pm on Sunday 30 May, and attended along with the ambulance service and fire service, who got the two-year-old boy out of the water.
He was subsequently taken to Southampton General Hospital where he sadly died today (Thursday 3 June).
Police say they are investigating the circumstances surrounding how the boy came to be in the water, and officers would like to hear from anyone who was in this area between 7.45pm and 8.30pm.
Detective Inspector Matt Gillooly, who is leading the investigation, said: “This is a very sad case, and our thoughts remain with the child’s family at this time.
“We are still trying to establish exactly how this boy came to be in the water, and we are keeping an open mind regarding the circumstances.
“As part of our investigation, we want to speak to everyone who was at the reserve between 7.45pm and 8.30pm. We know there was a female dogwalker with a small dog in the area at this time.
“Was this you? Please call us if you were there. Equally, we want to identify everyone who was there as any information, no matter how small, could prove significant.”
An 18-year-old man from Southampton, who is known to the boy, was arrested in connection with this incident as part of enquiries, and subsequently bailed until 27 June.
Anyone with information is asked to contact police on 101, quoting 44210210811.