They say the 4-month-old Syosset boy apparently stopped breathing after being put down for a nap around 11 a.m. Thursday.
Police say the owner of the Kay Shriver day care center in Levittown called 911 and began performing CPR.
The infant was pronounced dead at Nassau County Medical Center.
There appear to be no indications of criminality, a Nassau County Police Department spokesman told Newsday.
The medical examiner will determine the cause of death.