Looks like Superman's cape comes with a personal-space policy ... 'cause David Corenswet stepped in fast when a photographer got a little too close to "Supergirl" star Milly Alcock.

Check out the clip -- the Man of Steel went full Balls of Steel, activating his super senses Monday night at the premiere of the latest DC Universe flick in NYC after spotting a photographer reach out and touch Milly's back.

David wasted no time flying into action ... swooping around the crowd and seemingly making it clear the photog needed to keep a safer distance.

The moment's gone viral online, with fans eating up the real-life "Superman protecting Supergirl" energy. After all, if the guy playing Clark Kent shoots you that look, you're probably backing off pretty fast!

And if you think that was heroic, just wait until Milly starts throwing punches of her own when Supergirl blasts into theaters June 26!