Shocked shoppers witnessed a vicious knife fight in a supermarket car park on Sunday that left one man stumbling through the streets with a life-threatening stab wound.

The fight erupted just before 6pm when two men outside a Woolworths supermarket on Plenty Road in Preston South began arguing with each other.

One man grabbed a pole and bashed the other man, who then retaliated by pulling out a knife and stabbing him in the stomach, police said.

Witnesses reported seeing the bleeding man stumble through the inner-north car park at Preston South Shopping Centre and head into a residential area.

He made it at least three blocks as police and paramedics flooded the area.

The man, believed to be in his 40s, was then taken to the Royal Melbourne Hospital in a serious condition, an Ambulance Victoria spokesman said.

Police later arrested a Preston man, in his 30s, a police spokeswoman said.

He was being interviewed on Sunday night, but no charges have been laid at this time.