Police say officers were called around 3 p.m. Friday to a home near 36th Street and Camelback Road after the operator of the day care found the boy was not breathing.
The woman who runs the day care told police the infant was taking a nap and she went to wake him up.
Paramedics were unable to revive him and pronounced him dead.
Investigators say there were no signs of foul play.
The Maricopa County Medical Examiner's Office will conduct an autopsy to determine the cause of death.
Meanwhile, police are looking into whether the day care was licensed and how many children were in the home.
Copyright 2015 The Associated Press modified.