Injected @EJB is null in @Service Singleton's constructor in JBoss EAP 5.x

Issue

I have a JBoss Singleton implemented with @Service annotation, which uses the @EJB annotation to inject an EJB reference. The injected EJB variable is being used in the constructor. When it deploys, it throws a null pointer exception (NullPointerException). How do I specify that this service is dependent on the EJB? I thought the @EJB handled that. See Example code:

import org.jboss.ejb3.annotation.Service;
import javax.ejb.EJB;

@Service
public class ExampleService{
    @EJB
    ExampleEJB ejb;

    public ExampleService(){
         ejb.hello(); // getting null pointer here
    }
}