Michael Donnermeyer, a city spokesman, said the child suffered serious injuries while most adult were only lightly hurt.
Police arrested a 33 year man of English origin but with a German passport as well as his 55 year old female passenger after he drove his Volkswagon Golf through the security barriers which mark the start of the pedestrian area.
Immediately after the accident the car was searched for explosives, although none were found.
As yet it unclear whether the man was under the influence of alcohol, or whether it was a deliberate action however an eye witness told reporters, "It looked like he knew what he was doing."
There fewer fans in the area due to a lack of match action on Sunday.
Upto 750,000 fans have packed the area when Germany has played and more than 900,000 are expected when the hosts play Italy in the semi finals on Tuesday.