Detectives are hunting a man who punched a woman in the face during an unprovoked and random attack at a Brisbane shopping centre last week.

Two women were walking out of Big W at Calamvale Central on Brisbane's southside just before midday last Tuesday, March 10, when a man walked up behind them.

Police said the man called out to the women and when they turned around he punched one of them in the face, knocking her to the ground and sending her glasses flying.

Security camera footage showed the attacker calmly saunter away after the sickening assault, before he doubled back to meet up with a female companion outside the Big W store.