Shia LaBeouf was repeatedly PUNCHED IN THE HEAD by a shirtless, hairy-bellied man on a Vancouver sidewalk last week -- and TMZ has obtained footage of the brutal ass whooping.

It's unclear exactly what provoked the attack -- but we're told Shia originally got into it with the man inside a bar called Cinema Public House ... and after security kicked them both out, the man tore off his shirt and unleashed the fury all over Shia's face.

Moments after the attack, Shia tries to chase after the guy -- but someone who appears to be his friend holds him back, telling him, "You gotta lay low right now!"