CRJ-900 Captain reported executing a go-around after encountering wake turbulence on approach to EWR in trail of a B737.

Narrative

On approach for [Runway] 4R into EWR; we encountered wake turbulence at 3;000 ft behind a B737. We were on the LOC; cleared for the approach; but had not caught the GS. F/O was flying; when the aircraft started banking violently left and right. The AP disengaged due to the unusual attitude; and I; as PM; silenced the aural warnings with the AP Disc on the yoke. The F/O continued to try and maintain control of the aircraft through manual inputs. I made the command decision we needed break off the approach because the wake turbulence was not stopping. I looked left; VMC outside; and didn't see any traffic. I told the F/O to make a left turn; and then attempted to break into radio traffic to inform ATC. There was confusion with ATC on why we are turning left off the approach. After explaining what happened; the Controller vectored us around for another approach. On the ground we received a phone number to contact TRACON. I spoke to the Supervisor; and told him what had happened. I made it clear we had hit wake turbulence; the AP disengaged; and I made a pilot in command decision to break off the approach when we couldn't clear the wake turbulence. He suggested next time I declare an emergency; while taken the actions I did. Looking back on the incident; I didn't have much time to make a radio call because we were focused on aviating and navigating. I'm not sure of the cause for wake turbulence 3.5 miles behind a 737.