The 45-year-old "Captain America: Civil War" actor said he doesn't like exposing his three-year-old daughter to fame, reported E! online.
"Fatherhood is the most important thing in my life. I still don't expose my baby's face, just to protect her or anyone in my family (who's) a minor.
"I just think that's not my decision to make. You know what I mean? You don't need to be world famous just because your jackass did is," Renner said.
The actor recently posted a pic of himself with daughter Ava from the set of "Wind River," a thriller he is shooting with Elizabeth Olsen, but says she is too young to know if she will be interested in acting.