It happened on Stanley Street at the intersection with Mary Avenue and involved a Royal Carting truck.
The boy was pronounced dead at the scene, while the grandmother was rushed to Westchester Medical Center with serious injuries.
She later died at the hospital.
The names of the victims will not be released.
The investigation is ongoing, and Poughkeepsie Police Department is asking any witnesses to the collision to contact the Town of Poughkeepsie Police Department Traffic Enforcement Unit at 845-485-3680.
"The Town of Poughkeepsie Police Department extends our condolences to all affected by this tragedy," the department said in a statement.
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