Law enforcement tells TMZ ... a member of Stallone's private security team called police around 3:30 PM and told cops they had performed a citizen's arrest on a 22-year-old male who got past Sly's gates.
We're told the suspect claimed that he simply wanted some face time with "The Expendables" star -- who wasn't home at the time.
The LAPD eventually arrived at the scene -- where they took the man into custody and booked him for misdemeanor trespassing.
According to police, the man is still in custody and is being held on $2,500 bail.
