A mother has watched in a horror as a man jumped into her car and sped off with her six-month-old baby in the back seat in Melbourne's north.

The mother was standing next to her Mercedes station wagon as she waited to pick up her three eldest children from primary school when a man brazenly jumped into the front seat at the intersection of Ohea and Ross Street in Coburg and drove off, about 3pm on Tuesday.

Her six-month-old daughter, believed to be named Amira, was in a baby capsule in the back seat.

Another woman threw herself on the car's bonnet in an attempt to stop the thief.