At about 1:30 p.m., the father and son were getting out of their vehicle when someone in a four-door sedan drove up and fired multiple shots in the vehicle.
They had just returned home to the 14600 block of Des Plaines Street, according to a statement from Harvey Police Chief Gregory Thomas.
The 10-year-old was in intensive care at Christ Medical Center in Oak Lawn, Thomas said.
The father was not injured.
Harvey police continued to investigate Saturday evening.
Bullets from the shooting hit a nearby house and vehicle.