Jordan Coleman died Wednesday while he and seven other children were on a trip away from 3C's Day Academy in Sunrise, The Miami Herald reported.
Broward County Sheriff Al Lamberti ordered the closing Thursday.
"We have a family, and a lot of people with a lot of questions, and we need to answer all those questions," Dani Moschella, a spokeswoman for the sheriff's office, said. "A family is mourning the death of a young person who just turned 4. This is a tragic loss, and we have a lot of work to do."
The Herald said Broward County Child Care Licensing had cited Cecily Roberts, owner of the daycare center, for having more children than her license permitted. The newspaper said the record suggests Roberts might have asked her daughter to take the eight children out for the day because she feared another inspection.
Jordan was found in an SUV parked at an apartment complex where the children were apparently taken for a snack and a nap after going swimming. Jordan was somehow left in the car when the others went inside.