The Oscar-winner's middle child Seraphina begged aggressive photographers to leave her alone as her famous father, 40, tried to protect her while he picked her up from school in Los Angeles.
A source close to the 'Argo ' star told USMagazine.com  that he was not happy about the situation and repeatedly asked the "menacing" paparazzi, who were "all over" them, to back off before picking Seraphina up and sticking his leg out to demonstrate how much space they wanted.
The insider said: "She was asking for them to stop. The paps said they needed to be 'that close.'
"They were really swarming his daughter and yelling at her - yelling at a 4-year-old.
"It's terrible...This is a 4-year-old we're talking about. This is a pre-schooler on her way to school, not a star outside a nightclub."
The actor, who shares two other children, Violet, seven, and Samuel, one, with his actress wife Jennifer Garner , was said to be extremely distressed by the incident and felt it went too far.
Ben admitted in January that he doesn't want his children to become celebrities because he already thinks they are exposed too much.
He previously said: "I would do whatever I could to discourage that. My kids have enough issues of being exposed in ways that I don't want them to be exposed, in magazines and shows and stuff."