The boy's life is no longer in danger, legal sources said on Thursday, although there were fears for his life after the accident on Wednesday afternoon.
Iban fell into the water and was caught between the boat and land, suffering serious injuries to the chest.
His father, other passengers and Disneyland staff managed to save him.
Various sources on Thursday said that he had got up while the boat was still moving, despite announcements warning passengers not to do so.
An official inquiry into the causes of the accident has been opened.
Disneyland Paris is Europe's top tourist destination, with received 265 million visitors in the last 20 years and 16 million in 2012.
Wednesday's accident was not the first at Disneyland:
- In 2008 a young man hurt his head in a fall from a merry-go-round seven metres above ground;
- In 2010 a worker threw himself under a train and an employee of a subcontractor died while working on the It's a Small World ride;
- In 2011 five people were injured, one seriously, on the Big Thunder Mountain ride;
- In January this year four people were slightly injured in an accident on a steam train.