A 17-year-old boy found asleep in a shopping centre has been charged over a string of terrifying home invasions and car thefts across Melbourne where families were woken by balaclava-clad thieves and threatened with knives and iron bars.

The teenager is allegedly one of five offenders who forced their way into a family home in Mernda, in Melbourne's north in the early hours of Tuesday morning, attacking one man and stealing a BMW.

It was the latest violent home invasion in a city-wide crime spree that began on Sunday night when four men, described by police as being of African appearance, smashed their way into homes in Bentleigh East and Derrimut and carjacked a mother and child in Port Melbourne.

The Broadmeadows teen was charged with one count of aggravated burglary, three counts of home invasion, five counts of theft of motor vehicle and three counts of theft.

He has been remanded to appear at a children's court at a later date.