Affleck told E! News at the Producer's Guild of America Awards in Los Angeles on Saturday that "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."
Together, Affleck and Garner have three children - Violet, seven, Seraphina, four, and 11-month-old Samuel.
However, daddy Affleck did go on to admit that if his children are seriously interested in acting as they get older, he'll support whatever makes them happy.
He said: "You know, if you're interested in drama, there's great theatre classes and stuff and that's what's appropriate."
At the awards show, Affleck won the award for Outstanding Producer of Theatrical Motion Picture at the event. The actor and producer previously revealed he thinks his working life is "richer" because of his family life.
He explained: "They're the most important people in my life. Family is a wonderful thing, but it doesn't mean you can't do other stuff in your life. In fact, having a family makes whatever other thing you have that much richer. If it was just me, I'd be home alone and think, 'Well, something good happened at work', but it's much nicer to share it with people you love.
"I think any time you become a richer person you have more substance. I hope that happened to me with having a family, but you never know!"