UFC Hall-of-Famer Matt Hughes is at the center of a police investigation ... after a female bystander told cops she suffered a broken nose when the fighter went off on another man inside an Illinois bar.

TMZ has confirmed 37-year-old Hughes was named in a police report filed in Taylor Springs, IL ... stemming from an April 23 incident at a place called Trails End Bar and Grill.

According to a source who was inside the bar, Hughes got into an argument with a male bar patron ... which led to some forceful shoving.

Sources tell us ... the woman is alleging Hughes pushed the other man into her ... and she suffered a broken nose in the collision. TMZ obtained a photo of the woman's face taken after the incident.