The lug nuts began disappearing about a week ago, the Chicago Sun-Times reported.
No officers have been involved in road accidents because of the apparent vandalism, officials said.
"It's not funny," one Morgan Park District officer said Saturday. "You could lose control and run into a building or a person or another car."
No suspects had been identified, but officers also discovered a concrete slab in the Morgan Park District police parking lot painted with an anarchy symbol, officials said.