12:13 PM PT -- We've just obtained the mugshot of the suspect, Demonte Jackson.

Bun B got into a shoot-out inside his own home with an intruder who tried to make off with the rapper's wife's luxury car.

Law enforcement sources tell TMZ around 5:45 last night, there was a knock at Bun B's door ... his wife, Queenie, opened it -- thinking it was a possible delivery -- to find a masked man holding a gun on the other side. The intruder demanded valuables, and Queenie offered up her Audi in the garage.

Bun B heard the commotion from upstairs, grabbed his gun, and confronted the intruder as he was getting into the Audi. A shootout between the two ensued, and the intruder ran away ... leaving his gun behind.

We're told several hours later, the masked man showed up at a Houston-area hospital with a gunshot injury to his shoulder.

The man was treated and then arrested for 2 counts of aggravated robbery with a weapon and one count burglary.