The shootings occurred at the Jewish Community Campus at Overland Park and a nearby assisted living centre, Village Shalom, local media said.
Police said a suspect, a bearded white man in his 70s, was in custody.
A local hospital said it was treating a teenage boy for a gunshot wound and that he was in a critical condition.
Two victims were named by relatives as Dr. William Lewis Corporan and his 14-year-old grandson, Reat Griffin Underwood.
They were killed in the car park of the Jewish Community Campus. They were both Christian.
A third person, female victim was shot dead at Village Shalom, a retirement home several streets away from the community centre.
President Barack Obama called the shootings “heartbreaking” and pledged the full support of the federal government.
Local TV stations broadcast footage of police arresting a suspect at the scene.
The man appeared to shout “Heil Hitler” from the back of a police car.
Police said the suspect was not from the area, and that he used a shotgun in the attacks.
They are trying to establish whether he used other weapons in addition.
The attack took place just before the Jewish festival of Passover, but police have declined to say whether the incident is linked to anti-Semitism.
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