Thames Valley Police have asked witnesses who were queuing for the Coastguard Headquarters boat trip at around 1pm on Thursday to come forward.
A 27-year-old woman from Witham, Essex, was arrested on Thursday on suspicion of neglecting a child to cause unnecessary harm. She has been released on bail until July 26.
The baby boy died at the hospital on Sunday, police said.
Investigating officer Detective Constable Zoe Eele, from the Child Abuse Investigation Unit, said: “We are investigating a distressing incident involving a very young child at Legoland Windsor earlier this week.
“First and foremost, our thoughts go out to the family of the boy who unfortunately died in hospital after cardiac arrest. We support them as best we can during this extremely difficult time.
“We are working closely with the team at Legoland Windsor Resort but would like to speak to anyone who has information about this incident, particularly anyone who was queuing for the boat ride at Coastguard Headquarters between 11.30am and 12.45pm.
“We have made an arrest in connection with this incident and are not looking for anyone else as a suspect.
“I would ask the public to avoid speculation about the incident and respect the boy's family at this very disturbing time.”