Jake Gyllenhaal -- Check Out My New Bandages

Jake Gyllenhaal trotted out his bandage-wrapped hand in Hollywood yesterday ... just days after he was rushed to an ER for slicing his mitt on a mirror.

Jake attended a screening of "Prisoners" Friday night -- and laughed it up during a Q&A for his movie ... seemingly unfazed by the injury.

As we previously reported ... Gyllenhaal "flipped out" while filming a scene for a movie called "Nightcrawler" and punched a mirror.  The cut was so bad he needed stitches.

Not as bad as "Prince of Persia: The Sands of Time."