A judge on Monday ordered the arrest of Salvatore Anello after prosecutors submitted evidence and said the two-year-old girl fell when he raised her up to an open window.
A lawyer for the family has said Chloe Wiegand asked her grandfather to lift her up so she could bang on the glass in a children's play area.
He blamed the cruise ship company for leaving the window inexplicably open.
The family is from Indiana and was onboard Royal Caribbean's Freedom of the Seas docked in Puerto Rico in July.
Anello is being held on a £62,000 bond and is scheduled to appear in court on November 20.