Law enforcement sources tell us Joshua "Wash" Washington is the 23-year-old male who was shot and rushed to a local hospital by someone at the scene in the minutes following the melee ... cops described his injuries as non-life threatening.

Wash has been close with Quavo for years, and describes himself as Quavo's assistant and part of operations management at Huncho Records on his social media profile.

As we reported, there was also a 24-year-old female who was shot ... she was also taken to a hospital and treated for non-life-threatening injuries.

While the shooter (or shooters) have yet to be publicly named, the Harris County Medical Examiner's Office says Takeoff was shot in both the head and torso early Monday morning.

In video obtained by TMZ from the scene, you can see Quavo in an argument and then start to walk away as shots ring out. There's also video showing one man holding a gun to his side ... police have named that man as a person of interest in Takeoff's death.