I have a simple hierarchy like follows:
public abstract class AbsFoo {
    protected AbsBoo boo;
}
public class Foo extends AbsFoo {
    public Foo() {
        boo = new Boo(); // Boo extends AbsBoo
    }
} 
EDIT: Instances of AbsFoo should be created on the fly and may not be fields
Can I replace boo = new Boo() with injection?
Yes:
public abstract class AbsFoo {
    protected AbsBoo boo;
}
public class Foo extends AbsFoo {
    @Inject
    public Foo(Boo boo) {
        super.boo = boo; // Boo extends AbsBoo
    }
} 
Make sure you construct your Foo instance with @Inject or injector.getInstance()
Edit
You can also use a provider to create instances on demand:
@Inject
Provider<Foo> fooProvider
//...
public void doSomething(){
    //need new foo:
    Foo foo = fooProvider.get();
}
As long as Boo itself isn't abstract you should be able to.
public class Foo extends AbsFoo {
    @Inject
    public Foo( AbsBoo boo ) {
        this.boo = boo;
    }
}
public class FooModule extends AbstractModule {
  @Override 
  protected void configure() {
    bind(AbsBoo.class).to(Boo.class);
    bind(AbsFoo.class).to(Foo.class);
  }
}
public static void main(String[] args) {
    Injector injector = Guice.createInjector(new FooModule());
    AbsFoo foo = injector.getInstance(AbsFoo.class);
    ...
}
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