A man is on the run after another man in his 70s was randomly stabbed in a Melbourne park this morning.

The 71-year-old man was walking near Crighton Reserve in Port Melbourne about 5.20am when he approached by an unknown man and stabbed three times.

The Port Melbourne man fled to a nearby cafe on Bay Street where he raised the alarm.

"He wasn't too bad, you know, he could still talk...I was pleased about that. But he was bleeding, he lost a lot of blood," witness Mohammad Hassoun said.

"They done it for nothing, they didn't even try to take nothing from him, just stab and go."

He was rushed to hospital with serious but non-life-threatening injuries.

Despite a thorough search of the area, police have been unable to locate the offender.

He is described as Caucasian, aged between 30 and 40 years old, around 182cm tall, possibly with brown hair, wearing all black clothing.

"It is shocking to us and it's concerning considering the age of the victim and the location it's happened," Detective Senior Constable Georgia Herbert said.

"It was early in the morning, a lot of people are out walking their dogs at that time."

Anyone with information is urged to contact police.

It is the second random stabbing in just over 24 hours in Melbourne, after a teenager was charged over an alleged stabbing in Clayton yesterday.

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