Two of the children were pinned under the car, which wound up entirely inside the building, The Kansas City Star reported. The children's injuries were not believed to be life-threatening, a Children's Mercy Hospital spokeswoman told the newspaper.
The 80-year-old man driving the Range Rover sport utility vehicle also was taken to a hospital with injuries.
The crash occurred just before 1 p.m. at Christian Academy Day Care.
About 40 children were in the building when the accident happened.