Police allege the man allegedly entered the car and drove off, while the victim clung onto the bonnet.
Song and his partner BiBi Kim had left their Ford running while they were unloading groceries at their new apartment on Hardware Street.
He was left with serious injuries after he attempted to stop the theft.
“The doctor, who is in the hospital, said, ‘It’s a miracle. You’re very lucky, but unlucky’,” he told 9News.
“The tyre was (coming) over my head, and arms, and my chest here.
“Because I was rolled I thought, ‘I’m gonna be dead, I’m gonna be dead.'”
A 27-year-old man was arrested at an address on Elizabeth Street in Melbourne just before 2pm today.
He will now be interviewed by detectives.
Police said the allegedly stolen car remains outstanding at this stage.