GABRIEL AUBRY CAN'T BE TRUSTED ALONE ... WITH NAHLA

Gabriel Aubry is being watched ... watched by a monitor whenever he's with Nahla ... 'cause a judge ruled he can't be trusted with the child alone, at least for now.

TMZ broke the story ... Halle Berry's baby daddy was ordered into Dependency Court today after the L.A. Department of Children and Family Services concluded its investigation. As we reported, DCFS not only looked at an incident in which Gabriel allegedly pushed a nanny while she was holding Nahla, but other incidents as well.

We're told DCFS had information that Gabriel had yanked the baby from the nanny's arms on at least one occasion and screamed at Nahla multiple times.

We're told DCFS had extensive information that it had reviewed and then recommended a monitor for Gabriel when he has Nahla.

We're told .. the judge agreed this morning and put the monitor in place after a hearing.