'They Put a Gun Right In My Face'

One of the people robbed at gunpoint outside the UFC 224 host hotel in Brazil is a famous MMA manager, who tells TMZ Sports ... the robbers shoved their weapons right in their faces.

Very scary moment for Brian Butler-Au -- who manages big fighters like Max Holloway -- and is in Rio to support his fighter, Brian “BOOM” Kelleher, who's fighting on the main card at UFC 224.

Butler-Au says he was at a table on the beach with roughly 10 other people when the 3 men with guns rushed over and pulled out weapons.

"This guy walked up beside me ... he pulled out this handgun that had an extended magazine on it, put it up in my face and then he grabbed my phone."

Butler-Au says the 3 men -- none of whom…