Former NFL running back LeGarrette Blount was involved in a fight at a youth football game on Saturday ... throwing punches in a wild skirmish -- and now, TMZ Sports has learned cops are investigating it all.

The altercation happened following the conclusion of a 12-year-old-and-under game in Gilbert, Arizona.

Blount was coaching the GCYFC Gators against the Elite -- when in the postgame handshake line ... he appeared to take exception to something someone had said to him.

Drone video shows Blount became upset -- and motioned animatedly toward coaches on the opposing team for several moments. Eventually, he grew so irate that he took off in a dead sprint in an attempt to confront someone on the other sideline.

Blount was ultimately restrained -- but footage shot from the field level shows dozens of parents then jumped in between the sidelines and began arguing.

The verbal altercation grew more and more heated -- and that's when Blount ran in and was seen on video throwing two punches at a man in a white T-shirt.

He was pulled away from the area, but others in the crowd continued to argue and squabble. Finally, after several minutes, people dispersed.

Cops tell us they were called to the scene shortly after 7 PM "in relation to multiple reports of adults fighting during a youth football game."

We're told, though, the fight had concluded by the time officers arrived. No injuries were reported.

Police say they are investigating the incident and have described Blount as "an involved party."

Of course, this is not the first time Blount has thrown a right hand on a football field -- he famously clocked Boise State defensive lineman Byron Hout following a 2009 game when he was a member of the Univ. of Oregon football team. He was suspended from the Ducks over it all, but was reinstated later on.

Blount went on to have a solid career in the NFL -- winning three Super Bowl titles while rushing for 56 touchdowns in 132 games.

We reached out to Blount's rep ... so far, no word back.