Robert De Niro almost became a victim of the real-life Grinch -- a home intruder who was legit trying to steal the dude's Christmas presents ... just days before the holiday.

Law enforcement sources tell TMZ ... the actor's NYC home was broken into early Monday, at around 3:30 AM, by what cops say was a 30-year-old woman who pried his door and slunk inside. Not quite Dr. Seuss-esque (down the chimney) -- but still scary nonetheless.

We're told the woman was caught red-handed in the act ... cops say she was attempting to clean out the bottom of RDN's tree of gifts -- but Bobby D himself, who we're told was home with family, came down to confront her when he heard all the commotion.

As you can imagine, the police were called ... and NYPD says they recognized this perp immediately. Apparently, she's been arrested pretty recently for similar crimes -- we're told her long-running M.O. is to case houses and break-in, much like she did at De Niro's.

In this case ... they caught her, arrested her and took to her to jail. Sounds like they didn't wanna wait for her heart to grow three sizes and realize the error of her ways.