Blueface was stabbed during his boxing workout yesterday -- but we're told cops now have the man who they think is responsible for the attack in custody.

Law enforcement sources tell TMZ Hip Hop, 36-year-old Brandon Henry Snell was arrested and booked for felony assault with a deadly weapon Wednesday afternoon after turning himself in ... and is currently sitting in jail.

You can see in the video, Blueface and a man get into a physical fight ... with the man's Rottweiler jumping in the background along with the action.

The animal never got involved in the fight. For what it's worth, we're told the dog was with Snell when he surrendered ... and it hung out at the police station until a family member came to retrieve it.

As we previously reported, Blueface was inside the Kaminsky Boxing Gym in L.A.'s San Fernando Valley when he was accosted ... with the "Thotiana" rapper describing the incident as similar to being attacked by a "boogieman."

Blueface got on IG Thursday to update fans on his recovery process, where his 5-year-old son offered up some valuable life advice ... suggesting his dad hang up his gloves, at least in that particular gym.

The kid may have a point ... someone bringing a knife to a fistfight is totally cause for concern.