EXCLUSIVE

Barbra Streisand's female dog just got herself into serious trouble at 36,000 feet -- attacking a flight attendant aboard a billionaire's fancy private jet ... and it was so bad, the victim needed stitches.

The perp is a bitch named Sammie -- Barbra's 12-year-old Coton de Tulear ... who accompanied Streisand on Tuesday during a flight from NYC to DC on a PJ owned by billionaire investor Ron Perelman.

Our sources tell us ... a female flight attendant noticed the dog and went over to pet her, but Sammie snapped, biting the woman's hand ... puncturing the skin and opening a wound that required stitches.

We're told Barbra IMMEDIATELY apologized to both Ron and the flight attendant -- but everyone forgave her and the injured woman is expected to make a full recovery.