The documentation does not explain how to inject a static property because this is not supported in Simple Injector.
Static properties are typically a bad idea, because they hinder testability, cause Temporal Coupling, and can cause Captive Dependencies.
If a static property is required, you will have to inject the dependency yourself. You can do that in the Composition Root, right after you made all the registrations to the Container.
Example:
var container = new Container();
// Make registrations to container here:
container.Verify();
Utility.MyStaticProperty = container.GetInstance<IDependency>();
Under normal conditions, Simple Injector will detect these types of Lifestyle Mismatches, but it will not be able to do so when you inject this property yourself.