It is understood several other people, including the bus driver, were injured just before 3.30pm.
A tarpaulin is covering the white car at the corner of Mt Eden and Bellevue roads.
The child has been rushed to hospital with serious injuries.
The bus involved was a double-decker NZ Bus which is contracted to Auckland Transport. It was running on the 277 route heading down Mt Eden Rd toward the city and Britomart.
Diversions are in place at Valley and Onslow roads and police advise motorists to stay away from the area.
Serious crash unit investigators are at the scene.
Another crash is blocking two lanes of Auckland's motorway between Takanini and Manurewa.
A truck and a car collided, said fire service northern communications shift manager Karen Larking.
Fire services arrived at the crash at 3.15pm.
The NZ Transport Agency warned motorists to expect delays, saying the crash had blocked two northbound lanes after the Great South Road offramp.
Meanwhile, a burst water main is flooding the intersection of Khyber Pass Rd and Mountain Rd.
Senior Sergeant Danny Meade said there was a "significant" amount of water flowing down Khyber Pass Rd towards Broadway in Newmarket, which is causing disruption to traffic.
Authorities are on the scene and attempting to stem the flow.
Police don't yet know how long it will take to fix the water main, and are urging people to avoid the area, if possible.
