Yes - Deb nailed it (as usual)
The key distinction here is whether A) the Injection was the purpose for the visit, or B) the provider had to do a medical evaluation first, and then determined that an injection was needed. Since this is a new patient, it's likely that scenario B applies, in which case you can certainly bill for an E/M service with modifier 25 in addition to the injection procedures assuming both services are performed and documented sufficiently and are distinct, separately identifiable services. There's nothing wrong with that.
Now, if the patient has an appointment to come back in 3 months for another injection, and there is a brief assessment before the injection is given, that assessment is included in the procedure so you should not bill an E/M plus the injection for that. There is a certain E/M component that is inherent to all surgical procedures (not necessarily talking about procedures in the Operating Room, but talking about all procedures in the surgery section of CPT) so it wouldn't be appropriate to add an E/M code to the injection just because the provider did a brief history and assessment before the procedure.