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.
Ray Liotta sues skin care company over use of likeness
Boston schools pull out free condoms over wrapping complaints