Some media outlets posted pictures of Kutcher, 37, carrying his daughter while going out in Santa Barbara, California earlier this week, reported Ace Showbiz.
"Why is it so hard for publications to respect that I would like the identity of my child kept private for safety reasons? Please honour that," the "Two and a Half Men" alum posted on Twitter.
He also responded to a fan who commented on his posting, "@sunnybmw3 I may have chosen this business but my daughter didn't."
Kutcher and partner Mila Kunis have been vocal about protecting their daughter's privacy.