In footage which was widely shown on British media, Carragher is shown winding down the window of his car and spitting at another vehicle following Liverpool's 2-1 loss to Manchester United on Saturday.
Reports said that some of Carragher's spit hit the face of the girl, who was sitting in the passenger seat. A male voice can be heard saying "unlucky Jamie lad, 2-1!" before Carragher spits.
Carragher, 40, said he had apologised to the family, admitting he "lost (his) rag". He had been covering the game as an expert for British broadcaster Sky Sports.